From c42dea2aca02e6de761db143ec074c974f6c1c7f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Petr=C3=B4nio=20C=C3=A2ndido?= <petronio.candido@gmail.com>
Date: Fri, 28 Sep 2018 19:35:07 -0300
Subject: [PATCH] Improving documentation for the Interval and Probabilistic
 forecasts

---
 docs/build/doctrees/environment.pickle        | Bin 2164490 -> 2167898 bytes
 docs/build/doctrees/pyFTS.benchmarks.doctree  | Bin 370418 -> 370949 bytes
 docs/build/doctrees/pyFTS.common.doctree      | Bin 376714 -> 376891 bytes
 .../doctrees/pyFTS.probabilistic.doctree      | Bin 49396 -> 68317 bytes
 .../_modules/pyFTS/benchmarks/Measures.html   |  69 ++++---
 .../html/_modules/pyFTS/common/FuzzySet.html  |   9 +-
 .../build/html/_modules/pyFTS/common/fts.html |   4 +-
 .../html/_modules/pyFTS/models/chen.html      |   2 +-
 .../_modules/pyFTS/models/ismailefendi.html   |   2 +-
 .../html/_modules/pyFTS/models/sadaei.html    |   2 +-
 .../html/_modules/pyFTS/models/song.html      |   2 +-
 docs/build/html/_modules/pyFTS/models/yu.html |   2 +-
 .../ProbabilityDistribution.html              |  81 +++++++-
 .../_modules/pyFTS/probabilistic/kde.html     |   6 +
 docs/build/html/genindex.html                 |   2 +-
 docs/build/html/objects.inv                   | Bin 5585 -> 5584 bytes
 docs/build/html/pyFTS.benchmarks.html         |  10 +-
 docs/build/html/pyFTS.common.html             |   4 +-
 docs/build/html/pyFTS.probabilistic.html      | 184 ++++++++++++++++--
 docs/build/html/searchindex.js                |   2 +-
 pyFTS/benchmarks/Measures.py                  |  69 ++++---
 pyFTS/common/Membership.py                    |   2 +-
 pyFTS/common/fts.py                           |   4 +-
 .../probabilistic/ProbabilityDistribution.py  |  81 +++++++-
 pyFTS/probabilistic/kde.py                    |   6 +
 25 files changed, 432 insertions(+), 111 deletions(-)

diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
index 4f44043317b86db9c6511f6b783cc3460c3fe8d2..b127453b2648224596dd44e3076f938300b74e29 100644
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diff --git a/docs/build/doctrees/pyFTS.benchmarks.doctree b/docs/build/doctrees/pyFTS.benchmarks.doctree
index a2dc18027e087936efc807010cc5f4893477f578..02511848d3746b75b0272885f537718f2eb71588 100644
GIT binary patch
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delta 124
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diff --git a/docs/build/doctrees/pyFTS.common.doctree b/docs/build/doctrees/pyFTS.common.doctree
index 6aaf1d1503a271bc635a3500978a75d6a5e31212..12205ff5cff38d5aa64937b5742a89c2362d9c62 100644
GIT binary patch
delta 355
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diff --git a/docs/build/doctrees/pyFTS.probabilistic.doctree b/docs/build/doctrees/pyFTS.probabilistic.doctree
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diff --git a/docs/build/html/_modules/pyFTS/benchmarks/Measures.html b/docs/build/html/_modules/pyFTS/benchmarks/Measures.html
index 01187bf..d646a8a 100644
--- a/docs/build/html/_modules/pyFTS/benchmarks/Measures.html
+++ b/docs/build/html/_modules/pyFTS/benchmarks/Measures.html
@@ -81,7 +81,7 @@
 <span class="kn">import</span> <span class="nn">time</span>
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
-<span class="kn">from</span> <span class="nn">pyFTS.common</span> <span class="k">import</span> <span class="n">FuzzySet</span><span class="p">,</span><span class="n">SortedCollection</span>
+<span class="kn">from</span> <span class="nn">pyFTS.common</span> <span class="k">import</span> <span class="n">FuzzySet</span><span class="p">,</span> <span class="n">SortedCollection</span>
 <span class="kn">from</span> <span class="nn">pyFTS.probabilistic</span> <span class="k">import</span> <span class="n">ProbabilityDistribution</span>
 
 
@@ -97,10 +97,10 @@
     <span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
     <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">n</span><span class="o">-</span><span class="n">k</span><span class="p">):</span>
-        <span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span><span class="p">]</span><span class="o">-</span><span class="n">mu</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span><span class="o">+</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">):</span>
+        <span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">mu</span><span class="p">)</span>
 
-    <span class="k">return</span> <span class="mi">1</span><span class="o">/</span><span class="p">((</span><span class="n">n</span><span class="o">-</span><span class="n">k</span><span class="p">)</span><span class="o">*</span><span class="n">sigma</span><span class="p">)</span><span class="o">*</span><span class="n">s</span></div>
+    <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">((</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="n">s</span></div>
 
 
 <div class="viewcode-block" id="rmse"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.rmse">[docs]</a><span class="k">def</span> <span class="nf">rmse</span><span class="p">(</span><span class="n">targets</span><span class="p">,</span> <span class="n">forecasts</span><span class="p">):</span>
@@ -159,9 +159,9 @@
     <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">forecasts</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
         <span class="n">forecasts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span>
     <span class="k">if</span> <span class="nb">type</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">((</span><span class="n">forecasts</span> <span class="o">+</span> <span class="n">targets</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">((</span><span class="n">forecasts</span> <span class="o">+</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span>
     <span class="k">elif</span> <span class="nb">type</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">targets</span><span class="p">))</span> <span class="p">)</span><span class="o">*</span><span class="mi">100</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">targets</span><span class="p">)))</span> <span class="o">*</span> <span class="mi">100</span>
     <span class="k">else</span><span class="p">:</span>
         <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">-</span> <span class="n">targets</span><span class="p">))</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">forecasts</span> <span class="o">+</span> <span class="n">targets</span><span class="p">)</span></div>
 
@@ -187,8 +187,8 @@
 
     <span class="n">naive</span> <span class="o">=</span> <span class="p">[]</span>
     <span class="n">y</span> <span class="o">=</span> <span class="p">[]</span>
-    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">l</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
-        <span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">forecasts</span><span class="p">[</span><span class="n">k</span> <span class="p">]</span> <span class="o">-</span> <span class="n">targets</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">l</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+        <span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">forecasts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">targets</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
         <span class="n">naive</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">targets</span><span class="p">[</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">targets</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">naive</span><span class="p">))</span></div>
 
@@ -203,11 +203,10 @@
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">res</span> <span class="o">=</span> <span class="n">targets</span> <span class="o">-</span> <span class="n">forecasts</span>
     <span class="n">t</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
-    <span class="n">us</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">u</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">res</span><span class="p">]))</span>
-    <span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">targets</span><span class="p">]))</span>
-    <span class="n">fs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">f</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]))</span>
-    <span class="k">return</span>  <span class="n">us</span> <span class="o">/</span> <span class="p">(</span><span class="n">ys</span> <span class="o">+</span> <span class="n">fs</span><span class="p">)</span></div>
-
+    <span class="n">us</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">u</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">u</span> <span class="ow">in</span> <span class="n">res</span><span class="p">]))</span>
+    <span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">y</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">targets</span><span class="p">]))</span>
+    <span class="n">fs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">f</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">forecasts</span><span class="p">]))</span>
+    <span class="k">return</span> <span class="n">us</span> <span class="o">/</span> <span class="p">(</span><span class="n">ys</span> <span class="o">+</span> <span class="n">fs</span><span class="p">)</span></div>
 
 
 <div class="viewcode-block" id="BoxPierceStatistic"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.BoxPierceStatistic">[docs]</a><span class="k">def</span> <span class="nf">BoxPierceStatistic</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
@@ -220,10 +219,10 @@
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">h</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">h</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
         <span class="n">r</span> <span class="o">=</span> <span class="n">acf</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
-        <span class="n">s</span> <span class="o">+=</span> <span class="n">r</span><span class="o">**</span><span class="mi">2</span>
-    <span class="k">return</span> <span class="n">n</span><span class="o">*</span><span class="n">s</span></div>
+        <span class="n">s</span> <span class="o">+=</span> <span class="n">r</span> <span class="o">**</span> <span class="mi">2</span>
+    <span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="n">s</span></div>
 
 
 <div class="viewcode-block" id="BoxLjungStatistic"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.BoxLjungStatistic">[docs]</a><span class="k">def</span> <span class="nf">BoxLjungStatistic</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
@@ -236,10 +235,10 @@
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">h</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">h</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
         <span class="n">r</span> <span class="o">=</span> <span class="n">acf</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
-        <span class="n">s</span> <span class="o">+=</span> <span class="n">r</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span><span class="n">k</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">n</span><span class="o">*</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">s</span></div>
+        <span class="n">s</span> <span class="o">+=</span> <span class="n">r</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">n</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">s</span></div>
 
 
 <div class="viewcode-block" id="sharpness"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.sharpness">[docs]</a><span class="k">def</span> <span class="nf">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">):</span>
@@ -248,7 +247,6 @@
     <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span></div>
 
 
-
 <div class="viewcode-block" id="resolution"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.resolution">[docs]</a><span class="k">def</span> <span class="nf">resolution</span><span class="p">(</span><span class="n">forecasts</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Resolution - Standard deviation of the intervals&quot;&quot;&quot;</span>
     <span class="n">shp</span> <span class="o">=</span> <span class="n">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">)</span>
@@ -304,9 +302,9 @@
     <span class="k">if</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span> <span class="ow">and</span> <span class="n">target</span> <span class="o">&lt;</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
         <span class="k">return</span> <span class="n">delta</span>
     <span class="k">elif</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">target</span><span class="p">)</span><span class="o">/</span><span class="n">tau</span>
+        <span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">forecast</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">target</span><span class="p">)</span> <span class="o">/</span> <span class="n">tau</span>
     <span class="k">elif</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
-        <span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="p">(</span><span class="n">target</span> <span class="o">-</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">/</span><span class="n">tau</span></div>
+        <span class="k">return</span> <span class="n">delta</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">target</span> <span class="o">-</span> <span class="n">forecast</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="n">tau</span></div>
 
 
 <div class="viewcode-block" id="winkler_mean"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.winkler_mean">[docs]</a><span class="k">def</span> <span class="nf">winkler_mean</span><span class="p">(</span><span class="n">tau</span><span class="p">,</span> <span class="n">targets</span><span class="p">,</span> <span class="n">forecasts</span><span class="p">):</span>
@@ -335,7 +333,7 @@
             <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">score</span><span class="p">)</span>
         <span class="k">except</span> <span class="ne">ValueError</span> <span class="k">as</span> <span class="n">ex</span><span class="p">:</span>
             <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">sum</span><span class="p">([</span><span class="n">d</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">bins</span><span class="p">]))</span>
-    <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span></div>
+    <span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">ret</span><span class="p">)</span></div>
 
 
 <div class="viewcode-block" id="pmf_to_cdf"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.pmf_to_cdf">[docs]</a><span class="k">def</span> <span class="nf">pmf_to_cdf</span><span class="p">(</span><span class="n">density</span><span class="p">):</span>
@@ -345,7 +343,7 @@
         <span class="n">prev</span> <span class="o">=</span> <span class="mi">0</span>
         <span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="n">density</span><span class="o">.</span><span class="n">columns</span><span class="p">:</span>
             <span class="n">prev</span> <span class="o">+=</span> <span class="n">density</span><span class="p">[</span><span class="n">col</span><span class="p">][</span><span class="n">row</span><span class="p">]</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">density</span><span class="p">[</span><span class="n">col</span><span class="p">][</span><span class="n">row</span><span class="p">])</span> <span class="k">else</span> <span class="mi">0</span>
-            <span class="n">tmp</span><span class="o">.</span><span class="n">append</span><span class="p">(</span> <span class="n">prev</span> <span class="p">)</span>
+            <span class="n">tmp</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">prev</span><span class="p">)</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
     <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">ret</span><span class="p">,</span> <span class="n">columns</span><span class="o">=</span><span class="n">density</span><span class="o">.</span><span class="n">columns</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">df</span></div>
@@ -354,6 +352,7 @@
 <div class="viewcode-block" id="heavyside"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.heavyside">[docs]</a><span class="k">def</span> <span class="nf">heavyside</span><span class="p">(</span><span class="nb">bin</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
     <span class="k">return</span> <span class="mi">1</span> <span class="k">if</span> <span class="nb">bin</span> <span class="o">&gt;=</span> <span class="n">target</span> <span class="k">else</span> <span class="mi">0</span></div>
 
+
 <div class="viewcode-block" id="heavyside_cdf"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.heavyside_cdf">[docs]</a><span class="k">def</span> <span class="nf">heavyside_cdf</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">targets</span><span class="p">):</span>
     <span class="n">ret</span> <span class="o">=</span> <span class="p">[]</span>
     <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">targets</span><span class="p">:</span>
@@ -378,7 +377,7 @@
     <span class="n">l</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">densities</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">bins</span><span class="p">)</span>
     <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">densities</span><span class="p">)</span>
     <span class="k">for</span> <span class="n">ct</span><span class="p">,</span> <span class="n">df</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">densities</span><span class="p">):</span>
-        <span class="n">_crps</span> <span class="o">+=</span> <span class="nb">sum</span><span class="p">([(</span><span class="n">df</span><span class="o">.</span><span class="n">cummulative</span><span class="p">(</span><span class="nb">bin</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="mi">1</span> <span class="k">if</span> <span class="nb">bin</span> <span class="o">&gt;=</span> <span class="n">targets</span><span class="p">[</span><span class="n">ct</span><span class="p">]</span> <span class="k">else</span> <span class="mi">0</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="nb">bin</span> <span class="ow">in</span> <span class="n">df</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
+        <span class="n">_crps</span> <span class="o">+=</span> <span class="nb">sum</span><span class="p">([(</span><span class="n">df</span><span class="o">.</span><span class="n">cumulative</span><span class="p">(</span><span class="nb">bin</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="mi">1</span> <span class="k">if</span> <span class="nb">bin</span> <span class="o">&gt;=</span> <span class="n">targets</span><span class="p">[</span><span class="n">ct</span><span class="p">]</span> <span class="k">else</span> <span class="mi">0</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span> <span class="k">for</span> <span class="nb">bin</span> <span class="ow">in</span> <span class="n">df</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
 
     <span class="k">return</span> <span class="n">_crps</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">l</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span></div>
 
@@ -393,7 +392,7 @@
 <span class="sd">    :return: a list with the RMSE, SMAPE and U Statistic</span>
 <span class="sd">    &#39;&#39;&#39;</span>
 
-    <span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;steps_ahead&#39;</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+    <span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;steps_ahead&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;type&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;point&#39;</span>
 
     <span class="n">indexer</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;indexer&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
@@ -411,7 +410,7 @@
 
     <span class="k">if</span> <span class="n">steps_ahead</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
         <span class="n">forecasts</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">ndata</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-        
+
         <span class="k">if</span> <span class="n">model</span><span class="o">.</span><span class="n">is_multivariate</span> <span class="ow">and</span> <span class="n">model</span><span class="o">.</span><span class="n">has_seasonality</span><span class="p">:</span>
             <span class="n">ndata</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">indexer</span><span class="o">.</span><span class="n">get_data</span><span class="p">(</span><span class="n">ndata</span><span class="p">)</span>
         <span class="k">elif</span> <span class="n">model</span><span class="o">.</span><span class="n">is_multivariate</span><span class="p">:</span>
@@ -428,12 +427,12 @@
     <span class="k">else</span><span class="p">:</span>
         <span class="n">steps_ahead_sampler</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;steps_ahead_sampler&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
         <span class="n">nforecasts</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ndata</span><span class="p">)</span><span class="o">-</span><span class="n">steps_ahead</span><span class="p">,</span><span class="n">steps_ahead_sampler</span><span class="p">):</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ndata</span><span class="p">)</span> <span class="o">-</span> <span class="n">steps_ahead</span><span class="p">,</span> <span class="n">steps_ahead_sampler</span><span class="p">):</span>
             <span class="n">sample</span> <span class="o">=</span> <span class="n">ndata</span><span class="p">[</span><span class="n">k</span> <span class="o">-</span> <span class="n">model</span><span class="o">.</span><span class="n">order</span><span class="p">:</span> <span class="n">k</span><span class="p">]</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">sample</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
             <span class="n">nforecasts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
 
-        <span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span> <span class="mi">1</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">rmse</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">mape</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">UStatistic</span><span class="p">(</span><span class="n">ndata</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">steps_ahead_sampler</span><span class="p">],</span> <span class="n">nforecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
@@ -442,7 +441,7 @@
 
 
 <div class="viewcode-block" id="get_interval_statistics"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.get_interval_statistics">[docs]</a><span class="k">def</span> <span class="nf">get_interval_statistics</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;</span>
+    <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Condensate all measures for point interval forecasters</span>
 
 <span class="sd">    :param data: test data</span>
@@ -450,7 +449,7 @@
 <span class="sd">    :param kwargs:</span>
 <span class="sd">    :return: a list with the sharpness, resolution, coverage, .05 pinball mean,</span>
 <span class="sd">    .25 pinball mean, .75 pinball mean and .95 pinball mean.</span>
-<span class="sd">    &#39;&#39;&#39;</span>
+<span class="sd">    &quot;&quot;&quot;</span>
 
     <span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;steps_ahead&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;type&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;interval&#39;</span>
@@ -475,7 +474,7 @@
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">sample</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
             <span class="n">forecasts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
 
-        <span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="n">start</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">max_lag</span> <span class="o">+</span> <span class="n">steps_ahead</span> <span class="o">-</span> <span class="mi">1</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">sharpness</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">resolution</span><span class="p">(</span><span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">coverage</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">model</span><span class="o">.</span><span class="n">max_lag</span><span class="p">:],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
@@ -489,14 +488,14 @@
 
 
 <div class="viewcode-block" id="get_distribution_statistics"><a class="viewcode-back" href="../../../pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.get_distribution_statistics">[docs]</a><span class="k">def</span> <span class="nf">get_distribution_statistics</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39;</span>
+    <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Get CRPS statistic and time for a forecasting model</span>
 
 <span class="sd">    :param data: test data</span>
 <span class="sd">    :param model: FTS model with probabilistic forecasting capability</span>
 <span class="sd">    :param kwargs:</span>
 <span class="sd">    :return: a list with the CRPS and execution time</span>
-<span class="sd">    &#39;&#39;&#39;</span>
+<span class="sd">    &quot;&quot;&quot;</span>
     <span class="n">steps_ahead</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;steps_ahead&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;type&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s1">&#39;distribution&#39;</span>
 
@@ -524,8 +523,6 @@
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">_e1</span> <span class="o">-</span> <span class="n">_s1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
         <span class="n">ret</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">round</span><span class="p">(</span><span class="n">brier_score</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">start</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="n">skip</span><span class="p">],</span> <span class="n">forecasts</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
     <span class="k">return</span> <span class="n">ret</span></div>
-
-
 </pre></div>
 
           </div>
diff --git a/docs/build/html/_modules/pyFTS/common/FuzzySet.html b/docs/build/html/_modules/pyFTS/common/FuzzySet.html
index 2ea3b36..18ab7b9 100644
--- a/docs/build/html/_modules/pyFTS/common/FuzzySet.html
+++ b/docs/build/html/_modules/pyFTS/common/FuzzySet.html
@@ -146,17 +146,23 @@
 <span class="sd">    :param ordered_sets: a list with the fuzzy sets names ordered by their centroids.</span>
 <span class="sd">    :return: A list with the best fuzzy sets that may contain x</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="n">max_len</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">fuzzy_sets</span><span class="p">)</span>
+    <span class="n">max_len</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">fuzzy_sets</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
     <span class="n">first</span> <span class="o">=</span> <span class="mi">0</span>
     <span class="n">last</span> <span class="o">=</span> <span class="n">max_len</span>
 
     <span class="k">while</span> <span class="n">first</span> <span class="o">&lt;=</span> <span class="n">last</span><span class="p">:</span>
         <span class="n">midpoint</span> <span class="o">=</span> <span class="p">(</span><span class="n">first</span> <span class="o">+</span> <span class="n">last</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
+
         <span class="n">fs</span> <span class="o">=</span> <span class="n">ordered_sets</span><span class="p">[</span><span class="n">midpoint</span><span class="p">]</span>
         <span class="n">fs1</span> <span class="o">=</span> <span class="n">ordered_sets</span><span class="p">[</span><span class="n">midpoint</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="k">if</span> <span class="n">midpoint</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="k">else</span> <span class="n">ordered_sets</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">fs2</span> <span class="o">=</span> <span class="n">ordered_sets</span><span class="p">[</span><span class="n">midpoint</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="k">if</span> <span class="n">midpoint</span> <span class="o">&lt;</span> <span class="n">max_len</span> <span class="k">else</span> <span class="n">ordered_sets</span><span class="p">[</span><span class="n">max_len</span><span class="p">]</span>
+
         <span class="k">if</span> <span class="n">fuzzy_sets</span><span class="p">[</span><span class="n">fs1</span><span class="p">]</span><span class="o">.</span><span class="n">centroid</span> <span class="o">&lt;=</span> <span class="n">x</span> <span class="o">&lt;=</span> <span class="n">fuzzy_sets</span><span class="p">[</span><span class="n">fs2</span><span class="p">]</span><span class="o">.</span><span class="n">centroid</span><span class="p">:</span>
             <span class="k">return</span> <span class="p">(</span><span class="n">midpoint</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">midpoint</span><span class="p">,</span> <span class="n">midpoint</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="n">midpoint</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">return</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">midpoint</span> <span class="o">&gt;=</span> <span class="n">max_len</span><span class="p">:</span>
+            <span class="k">return</span> <span class="p">[</span><span class="n">max_len</span><span class="p">]</span>
         <span class="k">else</span><span class="p">:</span>
             <span class="k">if</span> <span class="n">x</span> <span class="o">&lt;</span> <span class="n">fuzzy_sets</span><span class="p">[</span><span class="n">fs</span><span class="p">]</span><span class="o">.</span><span class="n">centroid</span><span class="p">:</span>
                 <span class="n">last</span> <span class="o">=</span> <span class="n">midpoint</span> <span class="o">-</span> <span class="mi">1</span>
@@ -164,6 +170,7 @@
                 <span class="n">first</span> <span class="o">=</span> <span class="n">midpoint</span> <span class="o">+</span> <span class="mi">1</span>
 
 
+
 <div class="viewcode-block" id="fuzzyfy"><a class="viewcode-back" href="../../../pyFTS.common.html#pyFTS.common.FuzzySet.fuzzyfy">[docs]</a><span class="k">def</span> <span class="nf">fuzzyfy</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">partitioner</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    A general method for fuzzyfication.</span>
diff --git a/docs/build/html/_modules/pyFTS/common/fts.html b/docs/build/html/_modules/pyFTS/common/fts.html
index 0b2b63e..ae66fd4 100644
--- a/docs/build/html/_modules/pyFTS/common/fts.html
+++ b/docs/build/html/_modules/pyFTS/common/fts.html
@@ -240,7 +240,7 @@
 
 <span class="sd">        :param data: time series data with the minimal length equal to the max_lag of the model</span>
 <span class="sd">        :param kwargs: model specific parameters</span>
-<span class="sd">        :return: a list with the forecasted intervals</span>
+<span class="sd">        :return: a list with the prediction intervals</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s1">&#39;This model do not perform one step ahead interval forecasts!&#39;</span><span class="p">)</span></div>
 
@@ -250,7 +250,7 @@
 
 <span class="sd">        :param data: time series data with the minimal length equal to the max_lag of the model</span>
 <span class="sd">        :param kwargs: model specific parameters</span>
-<span class="sd">        :return: a list with the forecasted Probability Distributions</span>
+<span class="sd">        :return: a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions</span>
 <span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s1">&#39;This model do not perform one step ahead distribution forecasts!&#39;</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/models/chen.html b/docs/build/html/_modules/pyFTS/models/chen.html
index 485d328..4623c94 100644
--- a/docs/build/html/_modules/pyFTS/models/chen.html
+++ b/docs/build/html/_modules/pyFTS/models/chen.html
@@ -124,7 +124,7 @@
 
 <div class="viewcode-block" id="ConventionalFTS.train"><a class="viewcode-back" href="../../../pyFTS.models.html#pyFTS.models.chen.ConventionalFTS.train">[docs]</a>    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
 
-        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy_series</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sets</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
+        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">partitioner</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">partitioner</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;sets&#39;</span><span class="p">)</span>
         <span class="n">flrs</span> <span class="o">=</span> <span class="n">FLR</span><span class="o">.</span><span class="n">generate_non_recurrent_flrs</span><span class="p">(</span><span class="n">tmpdata</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">generate_flrg</span><span class="p">(</span><span class="n">flrs</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/models/ismailefendi.html b/docs/build/html/_modules/pyFTS/models/ismailefendi.html
index 2b85b82..007804a 100644
--- a/docs/build/html/_modules/pyFTS/models/ismailefendi.html
+++ b/docs/build/html/_modules/pyFTS/models/ismailefendi.html
@@ -136,7 +136,7 @@
 
 <div class="viewcode-block" id="ImprovedWeightedFTS.train"><a class="viewcode-back" href="../../../pyFTS.models.html#pyFTS.models.ismailefendi.ImprovedWeightedFTS.train">[docs]</a>    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ndata</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
 
-        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy_series</span><span class="p">(</span><span class="n">ndata</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sets</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
+        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy</span><span class="p">(</span><span class="n">ndata</span><span class="p">,</span> <span class="n">partitioner</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">partitioner</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;sets&#39;</span><span class="p">)</span>
         <span class="n">flrs</span> <span class="o">=</span> <span class="n">FLR</span><span class="o">.</span><span class="n">generate_recurrent_flrs</span><span class="p">(</span><span class="n">tmpdata</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">generate_flrg</span><span class="p">(</span><span class="n">flrs</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/models/sadaei.html b/docs/build/html/_modules/pyFTS/models/sadaei.html
index 80da7d0..de65e0a 100644
--- a/docs/build/html/_modules/pyFTS/models/sadaei.html
+++ b/docs/build/html/_modules/pyFTS/models/sadaei.html
@@ -140,7 +140,7 @@
                 <span class="bp">self</span><span class="o">.</span><span class="n">flrgs</span><span class="p">[</span><span class="n">flr</span><span class="o">.</span><span class="n">LHS</span><span class="p">]</span><span class="o">.</span><span class="n">append_rhs</span><span class="p">(</span><span class="n">flr</span><span class="o">.</span><span class="n">RHS</span><span class="p">)</span></div>
 
 <div class="viewcode-block" id="ExponentialyWeightedFTS.train"><a class="viewcode-back" href="../../../pyFTS.models.html#pyFTS.models.sadaei.ExponentialyWeightedFTS.train">[docs]</a>    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy_series</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sets</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
+        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">partitioner</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">partitioner</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;sets&#39;</span><span class="p">)</span>
         <span class="n">flrs</span> <span class="o">=</span> <span class="n">FLR</span><span class="o">.</span><span class="n">generate_recurrent_flrs</span><span class="p">(</span><span class="n">tmpdata</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">generate_flrg</span><span class="p">(</span><span class="n">flrs</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/models/song.html b/docs/build/html/_modules/pyFTS/models/song.html
index 91b1d9d..084cc08 100644
--- a/docs/build/html/_modules/pyFTS/models/song.html
+++ b/docs/build/html/_modules/pyFTS/models/song.html
@@ -124,7 +124,7 @@
 
 <div class="viewcode-block" id="ConventionalFTS.train"><a class="viewcode-back" href="../../../pyFTS.models.html#pyFTS.models.song.ConventionalFTS.train">[docs]</a>    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
 
-        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy_series</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sets</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
+        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">partitioner</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">partitioner</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;sets&#39;</span><span class="p">)</span>
         <span class="n">flrs</span> <span class="o">=</span> <span class="n">FLR</span><span class="o">.</span><span class="n">generate_non_recurrent_flrs</span><span class="p">(</span><span class="n">tmpdata</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">operation_matrix</span><span class="p">(</span><span class="n">flrs</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/models/yu.html b/docs/build/html/_modules/pyFTS/models/yu.html
index 7fea056..bd54588 100644
--- a/docs/build/html/_modules/pyFTS/models/yu.html
+++ b/docs/build/html/_modules/pyFTS/models/yu.html
@@ -132,7 +132,7 @@
                 <span class="bp">self</span><span class="o">.</span><span class="n">flrgs</span><span class="p">[</span><span class="n">flr</span><span class="o">.</span><span class="n">LHS</span><span class="p">]</span><span class="o">.</span><span class="n">append_rhs</span><span class="p">(</span><span class="n">flr</span><span class="o">.</span><span class="n">RHS</span><span class="p">)</span></div>
 
 <div class="viewcode-block" id="WeightedFTS.train"><a class="viewcode-back" href="../../../pyFTS.models.html#pyFTS.models.yu.WeightedFTS.train">[docs]</a>    <span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ndata</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy_series</span><span class="p">(</span><span class="n">ndata</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sets</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
+        <span class="n">tmpdata</span> <span class="o">=</span> <span class="n">FuzzySet</span><span class="o">.</span><span class="n">fuzzyfy</span><span class="p">(</span><span class="n">ndata</span><span class="p">,</span> <span class="n">partitioner</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">partitioner</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;maximum&#39;</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;sets&#39;</span><span class="p">)</span>
         <span class="n">flrs</span> <span class="o">=</span> <span class="n">FLR</span><span class="o">.</span><span class="n">generate_recurrent_flrs</span><span class="p">(</span><span class="n">tmpdata</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">generate_FLRG</span><span class="p">(</span><span class="n">flrs</span><span class="p">)</span></div>
 
diff --git a/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html b/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html
index dd830e1..cbe2d27 100644
--- a/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html
+++ b/docs/build/html/_modules/pyFTS/probabilistic/ProbabilityDistribution.html
@@ -135,10 +135,21 @@
         <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;name&quot;</span><span class="p">,</span> <span class="s2">&quot;&quot;</span><span class="p">)</span>
 
 <div class="viewcode-block" id="ProbabilityDistribution.set"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.set">[docs]</a>    <span class="k">def</span> <span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">density</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Assert a probability &#39;density&#39; for a certain value &#39;value&#39;, such that P(value) = density</span>
+
+<span class="sd">        :param value: A value in the universe of discourse from the distribution</span>
+<span class="sd">        :param density: The probability density to assign to the value</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">k</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bin_index</span><span class="o">.</span><span class="n">find_ge</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">density</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.append"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append">[docs]</a>    <span class="k">def</span> <span class="nf">append</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Increment the frequency count for the values</span>
+
+<span class="sd">        :param values: A list of values to account the frequency</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="s2">&quot;histogram&quot;</span><span class="p">:</span>
             <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">values</span><span class="p">:</span>
                 <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bin_index</span><span class="o">.</span><span class="n">find_ge</span><span class="p">(</span><span class="n">k</span><span class="p">)</span>
@@ -152,6 +163,11 @@
                 <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">[</span><span class="n">v</span><span class="p">]]</span> <span class="o">=</span> <span class="n">d</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.append_interval"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval">[docs]</a>    <span class="k">def</span> <span class="nf">append_interval</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">intervals</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Increment the frequency count for all values inside an interval</span>
+
+<span class="sd">        :param intervals: A list of intervals do increment the frequency</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">type</span> <span class="o">==</span> <span class="s2">&quot;histogram&quot;</span><span class="p">:</span>
             <span class="k">for</span> <span class="n">interval</span> <span class="ow">in</span> <span class="n">intervals</span><span class="p">:</span>
                 <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bin_index</span><span class="o">.</span><span class="n">inside</span><span class="p">(</span><span class="n">interval</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">interval</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
@@ -159,6 +175,12 @@
                     <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.density"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density">[docs]</a>    <span class="k">def</span> <span class="nf">density</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the probability densities for the input values</span>
+
+<span class="sd">        :param values: List of values to return the densities</span>
+<span class="sd">        :return: List of probability densities for the input values</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">ret</span> <span class="o">=</span> <span class="p">[]</span>
         <span class="n">scalar</span> <span class="o">=</span> <span class="kc">False</span>
 
@@ -183,6 +205,12 @@
         <span class="k">return</span> <span class="n">ret</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.differential_offset"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset">[docs]</a>    <span class="k">def</span> <span class="nf">differential_offset</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Auxiliary function for probability distributions of differentiated data</span>
+
+<span class="sd">        :param value:</span>
+<span class="sd">        :return:</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">nbins</span> <span class="o">=</span> <span class="p">[]</span>
         <span class="n">dist</span> <span class="o">=</span> <span class="p">{}</span>
 
@@ -201,6 +229,11 @@
         <span class="bp">self</span><span class="o">.</span><span class="n">qtl</span> <span class="o">=</span> <span class="kc">None</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.expected_value"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value">[docs]</a>    <span class="k">def</span> <span class="nf">expected_value</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the expected value of the distribution, as E[X] = ∑ x * P(x)</span>
+
+<span class="sd">        :return: The expected value of the distribution</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">nansum</span><span class="p">([</span><span class="n">v</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.build_cdf_qtl"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.build_cdf_qtl">[docs]</a>    <span class="k">def</span> <span class="nf">build_cdf_qtl</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
@@ -221,7 +254,13 @@
 
         <span class="bp">self</span><span class="o">.</span><span class="n">quantile_index</span> <span class="o">=</span> <span class="n">SortedCollection</span><span class="o">.</span><span class="n">SortedCollection</span><span class="p">(</span><span class="n">iterable</span><span class="o">=</span><span class="n">_keys</span><span class="p">)</span></div>
 
-<div class="viewcode-block" id="ProbabilityDistribution.cummulative"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cummulative">[docs]</a>    <span class="k">def</span> <span class="nf">cummulative</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
+<div class="viewcode-block" id="ProbabilityDistribution.cumulative"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative">[docs]</a>    <span class="k">def</span> <span class="nf">cumulative</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the cumulative probability densities for the input values</span>
+
+<span class="sd">        :param values: A list of input values</span>
+<span class="sd">        :return: The cumulative probability densities for the input values</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">cdf</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">build_cdf_qtl</span><span class="p">()</span>
 
@@ -235,6 +274,12 @@
             <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">cdf</span><span class="p">[</span><span class="n">values</span><span class="p">]</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.quantile"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile">[docs]</a>    <span class="k">def</span> <span class="nf">quantile</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the quantile values for the input values</span>
+
+<span class="sd">        :param values: input values</span>
+<span class="sd">        :return: The list of the quantile values for the input values</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">qtl</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             <span class="bp">self</span><span class="o">.</span><span class="n">build_cdf_qtl</span><span class="p">()</span>
 
@@ -250,21 +295,43 @@
         <span class="k">return</span> <span class="n">ret</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.entropy"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy">[docs]</a>    <span class="k">def</span> <span class="nf">entropy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the entropy of the probability distribution, H[X] =</span>
+
+<span class="sd">        :return:the entropy of the probability distribution</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">h</span> <span class="o">=</span> <span class="o">-</span><span class="nb">sum</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="k">else</span> <span class="mi">0</span>
                   <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
         <span class="k">return</span> <span class="n">h</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.crossentropy"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy">[docs]</a>    <span class="k">def</span> <span class="nf">crossentropy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">q</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Cross entropy between the actual probability distribution and the informed one.</span>
+
+<span class="sd">        :param q: a probabilistic.ProbabilityDistribution object</span>
+<span class="sd">        :return: Cross entropy between this probability distribution and the given distribution</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">h</span> <span class="o">=</span> <span class="o">-</span><span class="nb">sum</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">q</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="k">else</span> <span class="mi">0</span>
                   <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
         <span class="k">return</span> <span class="n">h</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.kullbackleiblerdivergence"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence">[docs]</a>    <span class="k">def</span> <span class="nf">kullbackleiblerdivergence</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span><span class="n">q</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Kullback-Leibler divergence between the actual probability distribution and the informed one.</span>
+
+<span class="sd">        :param q:  a probabilistic.ProbabilityDistribution object</span>
+<span class="sd">        :return: Kullback-Leibler divergence</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">h</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="o">/</span><span class="n">q</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="k">else</span> <span class="mi">0</span>
                   <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">])</span>
         <span class="k">return</span> <span class="n">h</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.empiricalloglikelihood"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood">[docs]</a>    <span class="k">def</span> <span class="nf">empiricalloglikelihood</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Empirical Log Likelihood of the probability distribution</span>
+
+<span class="sd">        :return:</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="n">_s</span> <span class="o">=</span> <span class="mi">0</span>
         <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">:</span>
             <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">distribution</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
@@ -272,6 +339,12 @@
         <span class="k">return</span> <span class="n">_s</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.pseudologlikelihood"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.pseudologlikelihood">[docs]</a>    <span class="k">def</span> <span class="nf">pseudologlikelihood</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Pseudo log likelihood of the probability distribution with respect to data</span>
+
+<span class="sd">        :param data:</span>
+<span class="sd">        :return:</span>
+<span class="sd">        &quot;&quot;&quot;</span>
 
         <span class="n">densities</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
 
@@ -282,6 +355,12 @@
         <span class="k">return</span> <span class="n">_s</span></div>
 
 <div class="viewcode-block" id="ProbabilityDistribution.averageloglikelihood"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood">[docs]</a>    <span class="k">def</span> <span class="nf">averageloglikelihood</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Average log likelihood of the probability distribution with respect to data</span>
+
+<span class="sd">        :param data:</span>
+<span class="sd">        :return:</span>
+<span class="sd">        &quot;&quot;&quot;</span>
 
         <span class="n">densities</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">density</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
 
diff --git a/docs/build/html/_modules/pyFTS/probabilistic/kde.html b/docs/build/html/_modules/pyFTS/probabilistic/kde.html
index 370fe66..1b2dc6b 100644
--- a/docs/build/html/_modules/pyFTS/probabilistic/kde.html
+++ b/docs/build/html/_modules/pyFTS/probabilistic/kde.html
@@ -92,6 +92,12 @@
         <span class="bp">self</span><span class="o">.</span><span class="n">transf</span> <span class="o">=</span> <span class="n">Transformations</span><span class="o">.</span><span class="n">Scale</span><span class="p">(</span><span class="nb">min</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="nb">max</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
 
 <div class="viewcode-block" id="KernelSmoothing.kernel_function"><a class="viewcode-back" href="../../../pyFTS.probabilistic.html#pyFTS.probabilistic.kde.KernelSmoothing.kernel_function">[docs]</a>    <span class="k">def</span> <span class="nf">kernel_function</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+        <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Apply the kernel</span>
+
+<span class="sd">        :param u:</span>
+<span class="sd">        :return:</span>
+<span class="sd">        &quot;&quot;&quot;</span>
         <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">kernel</span> <span class="o">==</span> <span class="s2">&quot;epanechnikov&quot;</span><span class="p">:</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="p">(</span><span class="mi">3</span><span class="o">/</span><span class="mi">4</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">u</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
             <span class="k">return</span> <span class="n">tmp</span> <span class="k">if</span> <span class="n">tmp</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="k">else</span> <span class="mi">0</span>
diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
index d3e38f4..cf59e77 100644
--- a/docs/build/html/genindex.html
+++ b/docs/build/html/genindex.html
@@ -362,7 +362,7 @@
 </li>
       <li><a href="pyFTS.benchmarks.html#pyFTS.benchmarks.Measures.crps">crps() (in module pyFTS.benchmarks.Measures)</a>
 </li>
-      <li><a href="pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cummulative">cummulative() (pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution method)</a>
+      <li><a href="pyFTS.probabilistic.html#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative">cumulative() (pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution method)</a>
 </li>
       <li><a href="pyFTS.common.html#pyFTS.common.Util.current_milli_time">current_milli_time() (in module pyFTS.common.Util)</a>
 </li>
diff --git a/docs/build/html/objects.inv b/docs/build/html/objects.inv
index d5cb636b98da828a1ee3f749a3c942a85c4da5fc..0bbabca4c84a5f083687a93cf00c14983714fd96 100644
GIT binary patch
delta 449
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z^}b!(dJ{KWJOb}g`>9BhJ&B$Y%JvDBvG#R&q}B4v^~|vE6}x_~HZ>{qsHkWWi#PP}
znadnJs$RV_$<G<Rx;qsjcGi4~Daxc#bAo?R$!W4ng~(5=T-ARAPYg$R!3iU`1L~9g
zw@38cjbn}i^S3`uz;%CH9#v9#{I~KAi|_t=Q-5lIcViD5{nGv{7LoZ;=NDGu=G~3m
zeRyLJ5mawn(oxvW!&zIxf6-1eB9)!r)nAmX`_lVL(bCaWSGM}7BV3kH_cvvhJEoa8
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r>0*(27u9~+ZC$^cPj7bS<6m@cWpwJd@$$1W#jgDR!D##!t{S(sOG@f|

delta 450
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zE^p@E*f}QDTmUkq(c2_+GjVxHkK9{N9bgAb2sdM!68bv8-pay|IOqUwMpq;%=Ffsf
sPr6uS-bJ;ac3ao)=F^*<`S=%|TN$1DZM^)fOtCA!e=r*V1tY$=B5#H8wEzGB

diff --git a/docs/build/html/pyFTS.benchmarks.html b/docs/build/html/pyFTS.benchmarks.html
index fb3a96d..2666697 100644
--- a/docs/build/html/pyFTS.benchmarks.html
+++ b/docs/build/html/pyFTS.benchmarks.html
@@ -1430,7 +1430,7 @@ Value: the measure value</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted Probability Distributions</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions</p>
 </td>
 </tr>
 </tbody>
@@ -1451,7 +1451,7 @@ Value: the measure value</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted intervals</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the prediction intervals</p>
 </td>
 </tr>
 </tbody>
@@ -1505,7 +1505,7 @@ Value: the measure value</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted Probability Distributions</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions</p>
 </td>
 </tr>
 </tbody>
@@ -1655,7 +1655,7 @@ Value: the measure value</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted Probability Distributions</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions</p>
 </td>
 </tr>
 </tbody>
@@ -1676,7 +1676,7 @@ Value: the measure value</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted intervals</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the prediction intervals</p>
 </td>
 </tr>
 </tbody>
diff --git a/docs/build/html/pyFTS.common.html b/docs/build/html/pyFTS.common.html
index 479e27f..613ee7e 100644
--- a/docs/build/html/pyFTS.common.html
+++ b/docs/build/html/pyFTS.common.html
@@ -1648,7 +1648,7 @@ when the LHS pattern is identified on time t.</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted Probability Distributions</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions</p>
 </td>
 </tr>
 </tbody>
@@ -1669,7 +1669,7 @@ when the LHS pattern is identified on time t.</p>
 </ul>
 </td>
 </tr>
-<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the forecasted intervals</p>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">a list with the prediction intervals</p>
 </td>
 </tr>
 </tbody>
diff --git a/docs/build/html/pyFTS.probabilistic.html b/docs/build/html/pyFTS.probabilistic.html
index a240e8c..9954767 100644
--- a/docs/build/html/pyFTS.probabilistic.html
+++ b/docs/build/html/pyFTS.probabilistic.html
@@ -118,17 +118,46 @@ If type is KDE the PDF is continuous</p>
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append">
 <code class="descname">append</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.append"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Increment the frequency count for the values</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>values</strong> – A list of values to account the frequency</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval">
 <code class="descname">append_interval</code><span class="sig-paren">(</span><em>intervals</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.append_interval"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Increment the frequency count for all values inside an interval</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>intervals</strong> – A list of intervals do increment the frequency</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood">
 <code class="descname">averageloglikelihood</code><span class="sig-paren">(</span><em>data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.averageloglikelihood"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Average log likelihood of the probability distribution with respect to data</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>data</strong> – </td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="attribute">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.bins">
@@ -144,42 +173,117 @@ If type is KDE the PDF is continuous</p>
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy">
 <code class="descname">crossentropy</code><span class="sig-paren">(</span><em>q</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.crossentropy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Cross entropy between the actual probability distribution and the informed one.</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>q</strong> – a probabilistic.ProbabilityDistribution object</td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">Cross entropy between this probability distribution and the given distribution</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
-<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cummulative">
-<code class="descname">cummulative</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.cummulative"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cummulative" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative">
+<code class="descname">cumulative</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.cumulative"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the cumulative probability densities for the input values</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>values</strong> – A list of input values</td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">The cumulative probability densities for the input values</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density">
 <code class="descname">density</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.density"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Return the probability densities for the input values</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>values</strong> – List of values to return the densities</td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">List of probability densities for the input values</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset">
 <code class="descname">differential_offset</code><span class="sig-paren">(</span><em>value</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.differential_offset"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Auxiliary function for probability distributions of differentiated data</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>value</strong> – </td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood">
 <code class="descname">empiricalloglikelihood</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.empiricalloglikelihood"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Empirical Log Likelihood of the probability distribution</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy">
 <code class="descname">entropy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.entropy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Return the entropy of the probability distribution, H[X] =</p>
+<p>:return:the entropy of the probability distribution</p>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value">
 <code class="descname">expected_value</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.expected_value"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Return the expected value of the distribution, as E[X] = ∑ x * P(x)</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">The expected value of the distribution</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence">
 <code class="descname">kullbackleiblerdivergence</code><span class="sig-paren">(</span><em>q</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.kullbackleiblerdivergence"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Kullback-Leibler divergence between the actual probability distribution and the informed one.</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>q</strong> – a probabilistic.ProbabilityDistribution object</td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">Kullback-Leibler divergence</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="attribute">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.labels">
@@ -195,17 +299,52 @@ If type is KDE the PDF is continuous</p>
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.pseudologlikelihood">
 <code class="descname">pseudologlikelihood</code><span class="sig-paren">(</span><em>data</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.pseudologlikelihood"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.pseudologlikelihood" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Pseudo log likelihood of the probability distribution with respect to data</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>data</strong> – </td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile">
 <code class="descname">quantile</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.quantile"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Return the quantile values for the input values</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>values</strong> – input values</td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">The list of the quantile values for the input values</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.set">
 <code class="descname">set</code><span class="sig-paren">(</span><em>value</em>, <em>density</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.set"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.set" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Assert a probability ‘density’ for a certain value ‘value’, such that P(value) = density</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
+<li><strong>value</strong> – A value in the universe of discourse from the distribution</li>
+<li><strong>density</strong> – The probability density to assign to the value</li>
+</ul>
+</td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="attribute">
 <dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.type">
@@ -246,7 +385,18 @@ If type is KDE the PDF is continuous</p>
 <dl class="method">
 <dt id="pyFTS.probabilistic.kde.KernelSmoothing.kernel_function">
 <code class="descname">kernel_function</code><span class="sig-paren">(</span><em>u</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/kde.html#KernelSmoothing.kernel_function"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing.kernel_function" title="Permalink to this definition">¶</a></dt>
-<dd></dd></dl>
+<dd><p>Apply the kernel</p>
+<table class="docutils field-list" frame="void" rules="none">
+<col class="field-name" />
+<col class="field-body" />
+<tbody valign="top">
+<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>u</strong> – </td>
+</tr>
+<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
+</tr>
+</tbody>
+</table>
+</dd></dl>
 
 <dl class="method">
 <dt id="pyFTS.probabilistic.kde.KernelSmoothing.probability">
diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js
index 1e04a06..aeb5a16 100644
--- a/docs/build/html/searchindex.js
+++ b/docs/build/html/searchindex.js
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- Fuzzy Time Series for Python","pyFTS","pyFTS package","pyFTS.benchmarks package","pyFTS.common package","pyFTS.data package","pyFTS.models package","pyFTS.models.ensemble package","pyFTS.models.multivariate package","pyFTS.models.nonstationary package","pyFTS.models.seasonal package","pyFTS.partitioners package","pyFTS.probabilistic package","pyFTS Quick Start"],titleterms:{FTS:13,airpasseng:5,arima:3,artifici:5,benchmark:3,bitcoin:5,chaotic:5,chen:6,cheng:6,cmean:11,cmsft:10,common:[4,5,8,9,10],composit:4,conf:2,content:[2,3,4,5,6,7,8,9,10,11,12],cvft:9,data:5,dataset:5,dowjon:5,enrol:5,ensembl:7,entropi:11,ethereum:5,eur:5,exampl:13,fcm:11,flr:[4,8],flrg:[4,8,9],fts:4,fuzzi:[0,13],fuzzyset:4,gbp:5,glass:5,grid:11,henon:5,hoft:6,honsft:9,how:[0,13],huarng:11,hwang:6,ift:6,index:0,inmet:5,instal:13,ismailefendi:6,kde:12,knn:3,librari:0,logistic_map:5,lorentz:5,mackei:5,measur:3,membership:4,model:[6,7,8,9,10],modul:[2,3,4,5,6,7,8,9,10,11,12],msft:10,multiseason:7,multivari:8,mvft:8,naiv:3,nasdaq:5,nonstationari:9,nsft:9,packag:[2,3,4,5,6,7,8,9,10,11,12],parallel_util:11,partition:[9,10,11],perturb:9,probabilist:12,probabilitydistribut:12,pwft:6,pyft:[0,1,2,3,4,5,6,7,8,9,10,11,12,13],pyftsa:[],python:0,quantreg:3,quick:13,refer:[0,13],residualanalysi:3,rossler:5,sadaei:6,season:10,seasonalindex:10,seri:[0,5,13],sft:10,singleton:11,sonda:5,song:6,sortedcollect:4,start:13,submodul:[2,3,4,5,6,7,8,9,10,11,12],subpackag:[2,6],sunspot:5,taiex:5,time:[0,5,13],transform:4,tree:4,usag:13,usd:5,util:[3,4,9,11],variabl:8,what:[0,13]}})
\ No newline at end of file
diff --git a/pyFTS/benchmarks/Measures.py b/pyFTS/benchmarks/Measures.py
index 2cae1a6..ca156fe 100644
--- a/pyFTS/benchmarks/Measures.py
+++ b/pyFTS/benchmarks/Measures.py
@@ -7,7 +7,7 @@ pyFTS module for common benchmark metrics
 import time
 import numpy as np
 import pandas as pd
-from pyFTS.common import FuzzySet,SortedCollection
+from pyFTS.common import FuzzySet, SortedCollection
 from pyFTS.probabilistic import ProbabilityDistribution
 
 
@@ -23,10 +23,10 @@ def acf(data, k):
     sigma = np.var(data)
     n = len(data)
     s = 0
-    for t in np.arange(0,n-k):
-        s += (data[t]-mu) * (data[t+k] - mu)
+    for t in np.arange(0, n - k):
+        s += (data[t] - mu) * (data[t + k] - mu)
 
-    return 1/((n-k)*sigma)*s
+    return 1 / ((n - k) * sigma) * s
 
 
 def rmse(targets, forecasts):
@@ -85,9 +85,9 @@ def smape(targets, forecasts, type=2):
     if isinstance(forecasts, list):
         forecasts = np.array(forecasts)
     if type == 1:
-        return np.mean(np.abs(forecasts - targets) / ((forecasts + targets)/2))
+        return np.mean(np.abs(forecasts - targets) / ((forecasts + targets) / 2))
     elif type == 2:
-        return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets)) )*100
+        return np.mean(np.abs(forecasts - targets) / (abs(forecasts) + abs(targets))) * 100
     else:
         return sum(np.abs(forecasts - targets)) / sum(forecasts + targets)
 
@@ -113,8 +113,8 @@ def UStatistic(targets, forecasts):
 
     naive = []
     y = []
-    for k in np.arange(0,l-1):
-        y.append((forecasts[k ] - targets[k]) ** 2)
+    for k in np.arange(0, l - 1):
+        y.append((forecasts[k] - targets[k]) ** 2)
         naive.append((targets[k + 1] - targets[k]) ** 2)
     return np.sqrt(sum(y) / sum(naive))
 
@@ -129,11 +129,10 @@ def TheilsInequality(targets, forecasts):
     """
     res = targets - forecasts
     t = len(res)
-    us = np.sqrt(sum([u**2 for u in res]))
-    ys = np.sqrt(sum([y**2 for y in targets]))
-    fs = np.sqrt(sum([f**2 for f in forecasts]))
-    return  us / (ys + fs)
-
+    us = np.sqrt(sum([u ** 2 for u in res]))
+    ys = np.sqrt(sum([y ** 2 for y in targets]))
+    fs = np.sqrt(sum([f ** 2 for f in forecasts]))
+    return us / (ys + fs)
 
 
 def BoxPierceStatistic(data, h):
@@ -146,10 +145,10 @@ def BoxPierceStatistic(data, h):
     """
     n = len(data)
     s = 0
-    for k in np.arange(1,h+1):
+    for k in np.arange(1, h + 1):
         r = acf(data, k)
-        s += r**2
-    return n*s
+        s += r ** 2
+    return n * s
 
 
 def BoxLjungStatistic(data, h):
@@ -162,10 +161,10 @@ def BoxLjungStatistic(data, h):
     """
     n = len(data)
     s = 0
-    for k in np.arange(1,h+1):
+    for k in np.arange(1, h + 1):
         r = acf(data, k)
-        s += r**2 / (n -k)
-    return n*(n-2)*s
+        s += r ** 2 / (n - k)
+    return n * (n - 2) * s
 
 
 def sharpness(forecasts):
@@ -174,7 +173,6 @@ def sharpness(forecasts):
     return np.mean(tmp)
 
 
-
 def resolution(forecasts):
     """Resolution - Standard deviation of the intervals"""
     shp = sharpness(forecasts)
@@ -230,9 +228,9 @@ def winkler_score(tau, target, forecast):
     if forecast[0] < target and target < forecast[1]:
         return delta
     elif forecast[0] > target:
-        return delta + 2*(forecast[0] - target)/tau
+        return delta + 2 * (forecast[0] - target) / tau
     elif forecast[1] < target:
-        return delta + 2*(target - forecast[1])/tau
+        return delta + 2 * (target - forecast[1]) / tau
 
 
 def winkler_mean(tau, targets, forecasts):
@@ -261,7 +259,7 @@ def brier_score(targets, densities):
             ret.append(score)
         except ValueError as ex:
             ret.append(sum([d.distribution[k] ** 2 for k in d.bins]))
-    return sum(ret)/len(ret)
+    return sum(ret) / len(ret)
 
 
 def pmf_to_cdf(density):
@@ -271,7 +269,7 @@ def pmf_to_cdf(density):
         prev = 0
         for col in density.columns:
             prev += density[col][row] if not np.isnan(density[col][row]) else 0
-            tmp.append( prev )
+            tmp.append(prev)
         ret.append(tmp)
     df = pd.DataFrame(ret, columns=density.columns)
     return df
@@ -280,6 +278,7 @@ def pmf_to_cdf(density):
 def heavyside(bin, target):
     return 1 if bin >= target else 0
 
+
 def heavyside_cdf(bins, targets):
     ret = []
     for t in targets:
@@ -304,7 +303,7 @@ def crps(targets, densities):
     l = len(densities[0].bins)
     n = len(densities)
     for ct, df in enumerate(densities):
-        _crps += sum([(df.cummulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins])
+        _crps += sum([(df.cumulative(bin) - (1 if bin >= targets[ct] else 0)) ** 2 for bin in df.bins])
 
     return _crps / float(l * n)
 
@@ -319,7 +318,7 @@ def get_point_statistics(data, model, **kwargs):
     :return: a list with the RMSE, SMAPE and U Statistic
     '''
 
-    steps_ahead = kwargs.get('steps_ahead',1)
+    steps_ahead = kwargs.get('steps_ahead', 1)
     kwargs['type'] = 'point'
 
     indexer = kwargs.get('indexer', None)
@@ -337,7 +336,7 @@ def get_point_statistics(data, model, **kwargs):
 
     if steps_ahead == 1:
         forecasts = model.predict(ndata, **kwargs)
-        
+
         if model.is_multivariate and model.has_seasonality:
             ndata = model.indexer.get_data(ndata)
         elif model.is_multivariate:
@@ -354,12 +353,12 @@ def get_point_statistics(data, model, **kwargs):
     else:
         steps_ahead_sampler = kwargs.get('steps_ahead_sampler', 1)
         nforecasts = []
-        for k in np.arange(model.order, len(ndata)-steps_ahead,steps_ahead_sampler):
+        for k in np.arange(model.order, len(ndata) - steps_ahead, steps_ahead_sampler):
             sample = ndata[k - model.order: k]
             tmp = model.predict(sample, **kwargs)
             nforecasts.append(tmp[-1])
 
-        start = model.max_lag + steps_ahead -1
+        start = model.max_lag + steps_ahead - 1
         ret.append(np.round(rmse(ndata[start:-1:steps_ahead_sampler], nforecasts), 2))
         ret.append(np.round(mape(ndata[start:-1:steps_ahead_sampler], nforecasts), 2))
         ret.append(np.round(UStatistic(ndata[start:-1:steps_ahead_sampler], nforecasts), 2))
@@ -368,7 +367,7 @@ def get_point_statistics(data, model, **kwargs):
 
 
 def get_interval_statistics(data, model, **kwargs):
-    '''
+    """
     Condensate all measures for point interval forecasters
 
     :param data: test data
@@ -376,7 +375,7 @@ def get_interval_statistics(data, model, **kwargs):
     :param kwargs:
     :return: a list with the sharpness, resolution, coverage, .05 pinball mean,
     .25 pinball mean, .75 pinball mean and .95 pinball mean.
-    '''
+    """
 
     steps_ahead = kwargs.get('steps_ahead', 1)
     kwargs['type'] = 'interval'
@@ -401,7 +400,7 @@ def get_interval_statistics(data, model, **kwargs):
             tmp = model.predict(sample, **kwargs)
             forecasts.append(tmp[-1])
 
-        start = model.max_lag + steps_ahead -1
+        start = model.max_lag + steps_ahead - 1
         ret.append(round(sharpness(forecasts), 2))
         ret.append(round(resolution(forecasts), 2))
         ret.append(round(coverage(data[model.max_lag:], forecasts), 2))
@@ -415,14 +414,14 @@ def get_interval_statistics(data, model, **kwargs):
 
 
 def get_distribution_statistics(data, model, **kwargs):
-    '''
+    """
     Get CRPS statistic and time for a forecasting model
 
     :param data: test data
     :param model: FTS model with probabilistic forecasting capability
     :param kwargs:
     :return: a list with the CRPS and execution time
-    '''
+    """
     steps_ahead = kwargs.get('steps_ahead', 1)
     kwargs['type'] = 'distribution'
 
@@ -450,5 +449,3 @@ def get_distribution_statistics(data, model, **kwargs):
         ret.append(round(_e1 - _s1, 3))
         ret.append(round(brier_score(data[start:-1:skip], forecasts), 3))
     return ret
-
-
diff --git a/pyFTS/common/Membership.py b/pyFTS/common/Membership.py
index 7a2355b..3561253 100644
--- a/pyFTS/common/Membership.py
+++ b/pyFTS/common/Membership.py
@@ -87,4 +87,4 @@ def singleton(x, parameters):
     :param parameters: a list with one real value
     :returns
     """
-    return x == parameters[0]
\ No newline at end of file
+    return x == parameters[0]
diff --git a/pyFTS/common/fts.py b/pyFTS/common/fts.py
index dd6f732..3783857 100644
--- a/pyFTS/common/fts.py
+++ b/pyFTS/common/fts.py
@@ -166,7 +166,7 @@ class FTS(object):
 
         :param data: time series data with the minimal length equal to the max_lag of the model
         :param kwargs: model specific parameters
-        :return: a list with the forecasted intervals
+        :return: a list with the prediction intervals
         """
         raise NotImplementedError('This model do not perform one step ahead interval forecasts!')
 
@@ -176,7 +176,7 @@ class FTS(object):
 
         :param data: time series data with the minimal length equal to the max_lag of the model
         :param kwargs: model specific parameters
-        :return: a list with the forecasted Probability Distributions
+        :return: a list with probabilistic.ProbabilityDistribution objects representing the forecasted Probability Distributions
         """
         raise NotImplementedError('This model do not perform one step ahead distribution forecasts!')
 
diff --git a/pyFTS/probabilistic/ProbabilityDistribution.py b/pyFTS/probabilistic/ProbabilityDistribution.py
index 5613975..ac8b76c 100644
--- a/pyFTS/probabilistic/ProbabilityDistribution.py
+++ b/pyFTS/probabilistic/ProbabilityDistribution.py
@@ -61,10 +61,21 @@ class ProbabilityDistribution(object):
         self.name = kwargs.get("name", "")
 
     def set(self, value, density):
+        """
+        Assert a probability 'density' for a certain value 'value', such that P(value) = density
+
+        :param value: A value in the universe of discourse from the distribution
+        :param density: The probability density to assign to the value
+        """
         k = self.bin_index.find_ge(value)
         self.distribution[k] = density
 
     def append(self, values):
+        """
+        Increment the frequency count for the values
+
+        :param values: A list of values to account the frequency
+        """
         if self.type == "histogram":
             for k in values:
                 v = self.bin_index.find_ge(k)
@@ -78,6 +89,11 @@ class ProbabilityDistribution(object):
                 self.distribution[self.bins[v]] = d
 
     def append_interval(self, intervals):
+        """
+        Increment the frequency count for all values inside an interval
+
+        :param intervals: A list of intervals do increment the frequency
+        """
         if self.type == "histogram":
             for interval in intervals:
                 for k in self.bin_index.inside(interval[0], interval[1]):
@@ -85,6 +101,12 @@ class ProbabilityDistribution(object):
                     self.count += 1
 
     def density(self, values):
+        """
+        Return the probability densities for the input values
+
+        :param values: List of values to return the densities
+        :return: List of probability densities for the input values
+        """
         ret = []
         scalar = False
 
@@ -109,6 +131,12 @@ class ProbabilityDistribution(object):
         return ret
 
     def differential_offset(self, value):
+        """
+        Auxiliary function for probability distributions of differentiated data
+
+        :param value:
+        :return:
+        """
         nbins = []
         dist = {}
 
@@ -127,6 +155,11 @@ class ProbabilityDistribution(object):
         self.qtl = None
 
     def expected_value(self):
+        """
+        Return the expected value of the distribution, as E[X] = ∑ x * P(x)
+
+        :return: The expected value of the distribution
+        """
         return np.nansum([v * self.distribution[v] for v in self.bins])
 
     def build_cdf_qtl(self):
@@ -147,7 +180,13 @@ class ProbabilityDistribution(object):
 
         self.quantile_index = SortedCollection.SortedCollection(iterable=_keys)
 
-    def cummulative(self, values):
+    def cumulative(self, values):
+        """
+        Return the cumulative probability densities for the input values
+
+        :param values: A list of input values
+        :return: The cumulative probability densities for the input values
+        """
         if self.cdf is None:
             self.build_cdf_qtl()
 
@@ -161,6 +200,12 @@ class ProbabilityDistribution(object):
             return self.cdf[values]
 
     def quantile(self, values):
+        """
+        Return the quantile values for the input values
+
+        :param values: input values
+        :return: The list of the quantile values for the input values
+        """
         if self.qtl is None:
             self.build_cdf_qtl()
 
@@ -176,21 +221,43 @@ class ProbabilityDistribution(object):
         return ret
 
     def entropy(self):
+        """
+        Return the entropy of the probability distribution, H[X] =
+
+        :return:the entropy of the probability distribution
+        """
         h = -sum([self.distribution[k] * np.log(self.distribution[k]) if self.distribution[k] > 0 else 0
                   for k in self.bins])
         return h
 
     def crossentropy(self,q):
+        """
+        Cross entropy between the actual probability distribution and the informed one.
+
+        :param q: a probabilistic.ProbabilityDistribution object
+        :return: Cross entropy between this probability distribution and the given distribution
+        """
         h = -sum([self.distribution[k] * np.log(q.distribution[k]) if self.distribution[k] > 0 else 0
                   for k in self.bins])
         return h
 
     def kullbackleiblerdivergence(self,q):
+        """
+        Kullback-Leibler divergence between the actual probability distribution and the informed one.
+
+        :param q:  a probabilistic.ProbabilityDistribution object
+        :return: Kullback-Leibler divergence
+        """
         h = sum([self.distribution[k] * np.log(self.distribution[k]/q.distribution[k]) if self.distribution[k] > 0 else 0
                   for k in self.bins])
         return h
 
     def empiricalloglikelihood(self):
+        """
+        Empirical Log Likelihood of the probability distribution
+
+        :return:
+        """
         _s = 0
         for k in self.bins:
             if self.distribution[k] > 0:
@@ -198,6 +265,12 @@ class ProbabilityDistribution(object):
         return _s
 
     def pseudologlikelihood(self, data):
+        """
+        Pseudo log likelihood of the probability distribution with respect to data
+
+        :param data:
+        :return:
+        """
 
         densities = self.density(data)
 
@@ -208,6 +281,12 @@ class ProbabilityDistribution(object):
         return _s
 
     def averageloglikelihood(self, data):
+        """
+        Average log likelihood of the probability distribution with respect to data
+
+        :param data:
+        :return:
+        """
 
         densities = self.density(data)
 
diff --git a/pyFTS/probabilistic/kde.py b/pyFTS/probabilistic/kde.py
index 9eb95b5..b5c668f 100644
--- a/pyFTS/probabilistic/kde.py
+++ b/pyFTS/probabilistic/kde.py
@@ -18,6 +18,12 @@ class KernelSmoothing(object):
         self.transf = Transformations.Scale(min=0,max=1)
 
     def kernel_function(self, u):
+        """
+        Apply the kernel
+
+        :param u:
+        :return:
+        """
         if self.kernel == "epanechnikov":
             tmp = (3/4)*(1.0 - u**2)
             return tmp if tmp > 0 else 0