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<li><a class="reference internal" href="#">pyFTS.probabilistic package</a><ul>
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<li><a class="reference internal" href="#module-pyFTS.probabilistic.ProbabilityDistribution">pyFTS.probabilistic.ProbabilityDistribution module</a></li>
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<li><a class="reference internal" href="#module-pyFTS.probabilistic.kde">pyFTS.probabilistic.kde module</a></li>
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<div class="section" id="pyfts-probabilistic-package">
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<h1>pyFTS.probabilistic package<a class="headerlink" href="#pyfts-probabilistic-package" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="module-pyFTS.probabilistic">
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<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-pyFTS.probabilistic" title="Permalink to this headline">¶</a></h2>
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<p>Probability Distribution objects</p>
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</div>
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<div class="section" id="submodules">
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<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this headline">¶</a></h2>
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</div>
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<div class="section" id="module-pyFTS.probabilistic.ProbabilityDistribution">
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<span id="pyfts-probabilistic-probabilitydistribution-module"></span><h2>pyFTS.probabilistic.ProbabilityDistribution module<a class="headerlink" href="#module-pyFTS.probabilistic.ProbabilityDistribution" title="Permalink to this headline">¶</a></h2>
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<dl class="class">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution">
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<em class="property">class </em><code class="descclassname">pyFTS.probabilistic.ProbabilityDistribution.</code><code class="descname">ProbabilityDistribution</code><span class="sig-paren">(</span><em>type='KDE'</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution" title="Permalink to this definition">¶</a></dt>
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<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.8)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
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<p>Represents a discrete or continous probability distribution
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If type is histogram, the PDF is discrete
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If type is KDE the PDF is continuous</p>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append">
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<code class="descname">append</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append" title="Permalink to this definition">¶</a></dt>
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<dd><p>Increment the frequency count for the values</p>
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<table class="docutils field-list" frame="void" rules="none">
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<col class="field-name" />
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<col class="field-body" />
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<tbody valign="top">
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<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>
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</tr>
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</tbody>
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</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval">
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<code class="descname">append_interval</code><span class="sig-paren">(</span><em>intervals</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval" title="Permalink to this definition">¶</a></dt>
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<dd><p>Increment the frequency count for all values inside an interval</p>
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<table class="docutils field-list" frame="void" rules="none">
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<col class="field-name" />
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<col class="field-body" />
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<tbody valign="top">
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<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>
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</tr>
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</tbody>
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</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood">
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<code class="descname">averageloglikelihood</code><span class="sig-paren">(</span><em>data</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood" title="Permalink to this definition">¶</a></dt>
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<dd><p>Average log likelihood of the probability distribution with respect to data</p>
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<table class="docutils field-list" frame="void" rules="none">
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<col class="field-name" />
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<col class="field-body" />
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<tbody valign="top">
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>data</strong> – </td>
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</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
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</tr>
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</tbody>
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</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.build_cdf_qtl">
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<code class="descname">build_cdf_qtl</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.build_cdf_qtl" title="Permalink to this definition">¶</a></dt>
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<dd></dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy">
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<code class="descname">crossentropy</code><span class="sig-paren">(</span><em>q</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy" title="Permalink to this definition">¶</a></dt>
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<dd><p>Cross entropy between the actual probability distribution and the informed one,
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H(P,Q) = - ∑ P(x) log ( Q(x) )</p>
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<table class="docutils field-list" frame="void" rules="none">
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<col class="field-name" />
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<col class="field-body" />
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<tbody valign="top">
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>q</strong> – a probabilistic.ProbabilityDistribution object</td>
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</tr>
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<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>
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</tr>
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</tbody>
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</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative">
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<code class="descname">cumulative</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative" title="Permalink to this definition">¶</a></dt>
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<dd><p>Return the cumulative probability densities for the input values,
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such that F(x) = P(X <= x)</p>
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<table class="docutils field-list" frame="void" rules="none">
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||
<col class="field-name" />
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||
<col class="field-body" />
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||
<tbody valign="top">
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||
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>values</strong> – A list of input values</td>
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</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">The cumulative probability densities for the input values</td>
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</tr>
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</tbody>
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</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density">
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<code class="descname">density</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density" title="Permalink to this definition">¶</a></dt>
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<dd><p>Return the probability densities for the input values</p>
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||
<table class="docutils field-list" frame="void" rules="none">
|
||
<col class="field-name" />
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<col class="field-body" />
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||
<tbody valign="top">
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<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>
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</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">List of probability densities for the input values</td>
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</tr>
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</tbody>
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||
</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset">
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<code class="descname">differential_offset</code><span class="sig-paren">(</span><em>value</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset" title="Permalink to this definition">¶</a></dt>
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<dd><p>Auxiliary function for probability distributions of differentiated data</p>
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<table class="docutils field-list" frame="void" rules="none">
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||
<col class="field-name" />
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||
<col class="field-body" />
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||
<tbody valign="top">
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>value</strong> – </td>
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</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
|
||
</tr>
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||
</tbody>
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||
</table>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood">
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<code class="descname">empiricalloglikelihood</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood" title="Permalink to this definition">¶</a></dt>
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<dd><p>Empirical Log Likelihood of the probability distribution, L(P) = ∑ log( P(x) )</p>
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<table class="docutils field-list" frame="void" rules="none">
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||
<col class="field-name" />
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||
<col class="field-body" />
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||
<tbody valign="top">
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||
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"></td>
|
||
</tr>
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||
</tbody>
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||
</table>
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</dd></dl>
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||
|
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy">
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<code class="descname">entropy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy" title="Permalink to this definition">¶</a></dt>
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<dd><p>Return the entropy of the probability distribution, H(P) = E[ -ln P(X) ] = - ∑ P(x) log ( P(x) )</p>
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<p>:return:the entropy of the probability distribution</p>
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</dd></dl>
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<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value">
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<code class="descname">expected_value</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value" title="Permalink to this definition">¶</a></dt>
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<dd><p>Return the expected value of the distribution, as E[X] = ∑ x * P(x)</p>
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||
<table class="docutils field-list" frame="void" rules="none">
|
||
<col class="field-name" />
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||
<col class="field-body" />
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||
<tbody valign="top">
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||
<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>
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||
</dd></dl>
|
||
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<dl class="method">
|
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence">
|
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<code class="descname">kullbackleiblerdivergence</code><span class="sig-paren">(</span><em>q</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence" title="Permalink to this definition">¶</a></dt>
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<dd><p>Kullback-Leibler divergence between the actual probability distribution and the informed one.
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||
DKL(P || Q) = - ∑ P(x) log( P(X) / Q(x) )</p>
|
||
<table class="docutils field-list" frame="void" rules="none">
|
||
<col class="field-name" />
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||
<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>
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</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">Kullback-Leibler divergence</td>
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||
</tr>
|
||
</tbody>
|
||
</table>
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||
</dd></dl>
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|
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<dl class="method">
|
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.plot">
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<code class="descname">plot</code><span class="sig-paren">(</span><em>axis=None, color='black', tam=[10, 6], title=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.plot" title="Permalink to this definition">¶</a></dt>
|
||
<dd></dd></dl>
|
||
|
||
<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="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.pseudologlikelihood" title="Permalink to this definition">¶</a></dt>
|
||
<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" />
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||
<tbody valign="top">
|
||
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>data</strong> – </td>
|
||
</tr>
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<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
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||
</dd></dl>
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||
|
||
<dl class="method">
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<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile">
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<code class="descname">quantile</code><span class="sig-paren">(</span><em>values</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile" title="Permalink to this definition">¶</a></dt>
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<dd><p>Return the Universe of Discourse values in relation to the quantile input values,
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||
such that Q(tau) = min( {x | F(x) >= tau })</p>
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||
<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>
|
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</tr>
|
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<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">
|
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<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="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.set" title="Permalink to this definition">¶</a></dt>
|
||
<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>
|
||
|
||
</dd></dl>
|
||
|
||
<dl class="function">
|
||
<dt id="pyFTS.probabilistic.ProbabilityDistribution.from_point">
|
||
<code class="descclassname">pyFTS.probabilistic.ProbabilityDistribution.</code><code class="descname">from_point</code><span class="sig-paren">(</span><em>x</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.from_point" title="Permalink to this definition">¶</a></dt>
|
||
<dd><p>Create a probability distribution from a scalar value</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 simple">
|
||
<li><strong>x</strong> – scalar value</li>
|
||
<li><strong>kwargs</strong> – common parameters of the distribution</li>
|
||
</ul>
|
||
</td>
|
||
</tr>
|
||
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last">the ProbabilityDistribution object</p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</dd></dl>
|
||
|
||
</div>
|
||
<div class="section" id="module-pyFTS.probabilistic.kde">
|
||
<span id="pyfts-probabilistic-kde-module"></span><h2>pyFTS.probabilistic.kde module<a class="headerlink" href="#module-pyFTS.probabilistic.kde" title="Permalink to this headline">¶</a></h2>
|
||
<p>Kernel Density Estimation</p>
|
||
<dl class="class">
|
||
<dt id="pyFTS.probabilistic.kde.KernelSmoothing">
|
||
<em class="property">class </em><code class="descclassname">pyFTS.probabilistic.kde.</code><code class="descname">KernelSmoothing</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing" title="Permalink to this definition">¶</a></dt>
|
||
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.8)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
|
||
<p>Kernel Density Estimation</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="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing.kernel_function" title="Permalink to this definition">¶</a></dt>
|
||
<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">
|
||
<code class="descname">probability</code><span class="sig-paren">(</span><em>x</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing.probability" title="Permalink to this definition">¶</a></dt>
|
||
<dd><p>Probability of the point x on 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"><ul class="first simple">
|
||
<li><strong>x</strong> – </li>
|
||
<li><strong>data</strong> – </li>
|
||
</ul>
|
||
</td>
|
||
</tr>
|
||
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"></p>
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</dd></dl>
|
||
|
||
</dd></dl>
|
||
|
||
</div>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="clearer"></div>
|
||
</div>
|
||
<div class="related" role="navigation" aria-label="related navigation">
|
||
<h3>Navigation</h3>
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||
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<li class="right" style="margin-right: 10px">
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<a href="genindex.html" title="General Index"
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>index</a></li>
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||
>modules</a> |</li>
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