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<div class="section" id="pyfts-probabilistic-package">
<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">
<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-pyFTS.probabilistic" title="Permalink to this headline"></a></h2>
<p>Probability Distribution objects</p>
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<div class="section" id="module-pyFTS.probabilistic.ProbabilityDistribution">
<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>
<dl class="py class">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution">
<em class="property">class </em><code class="sig-prename descclassname">pyFTS.probabilistic.ProbabilityDistribution.</code><code class="sig-name descname">ProbabilityDistribution</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">type</span><span class="o">=</span><span class="default_value">'KDE'</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution" 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 v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Represents a discrete or continous probability distribution
If type is histogram, the PDF is discrete
If type is KDE the PDF is continuous</p>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append">
<code class="sig-name descname">append</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span></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><p>Increment the frequency count for the values</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>values</strong> – A list of values to account the frequency</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.append_interval">
<code class="sig-name descname">append_interval</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">intervals</span></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><p>Increment the frequency count for all values inside an interval</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>intervals</strong> – A list of intervals do increment the frequency</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.averageloglikelihood">
<code class="sig-name descname">averageloglikelihood</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">data</span></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><p>Average log likelihood of the probability distribution with respect to data</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>data</strong> – </p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p></p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.bins">
<code class="sig-name descname">bins</code><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.bins" title="Permalink to this definition"></a></dt>
<dd><p>Number of bins on a discrete PDF</p>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.build_cdf_qtl">
<code class="sig-name descname">build_cdf_qtl</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.build_cdf_qtl"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.build_cdf_qtl" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.crossentropy">
<code class="sig-name descname">crossentropy</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">q</span></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><p>Cross entropy between the actual probability distribution and the informed one,
H(P,Q) = - ∑ P(x) log ( Q(x) )</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>q</strong> – a probabilistic.ProbabilityDistribution object</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Cross entropy between this probability distribution and the given distribution</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.cumulative">
<code class="sig-name descname">cumulative</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span></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,
such that F(x) = P(X &lt;= x)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>values</strong> – A list of input values</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>The cumulative probability densities for the input values</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.density">
<code class="sig-name descname">density</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span></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><p>Return the probability densities for the input values</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>values</strong> – List of values to return the densities</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>List of probability densities for the input values</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.differential_offset">
<code class="sig-name descname">differential_offset</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">value</span></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><p>Auxiliary function for probability distributions of differentiated data</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>value</strong> – </p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.empiricalloglikelihood">
<code class="sig-name 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><p>Empirical Log Likelihood of the probability distribution, L(P) = ∑ log( P(x) )</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.entropy">
<code class="sig-name 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><p>Return the entropy of the probability distribution, H(P) = E[ -ln P(X) ] = - ∑ P(x) log ( P(x) )</p>
<p>:return:the entropy of the probability distribution</p>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.expected_value">
<code class="sig-name 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><p>Return the expected value of the distribution, as E[X] = ∑ x * P(x)</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>The expected value of the distribution</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.kullbackleiblerdivergence">
<code class="sig-name descname">kullbackleiblerdivergence</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">q</span></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><p>Kullback-Leibler divergence between the actual probability distribution and the informed one.
DKL(P || Q) = - ∑ P(x) log( P(X) / Q(x) )</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>q</strong> – a probabilistic.ProbabilityDistribution object</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Kullback-Leibler divergence</p>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.labels">
<code class="sig-name descname">labels</code><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.labels" title="Permalink to this definition"></a></dt>
<dd><p>Bins labels on a discrete PDF</p>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.plot">
<code class="sig-name descname">plot</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">axis</span><span class="o">=</span><span class="default_value">None</span></em>, <em class="sig-param"><span class="n">color</span><span class="o">=</span><span class="default_value">'black'</span></em>, <em class="sig-param"><span class="n">tam</span><span class="o">=</span><span class="default_value">[10, 6]</span></em>, <em class="sig-param"><span class="n">title</span><span class="o">=</span><span class="default_value">None</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#ProbabilityDistribution.plot"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.plot" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.pseudologlikelihood">
<code class="sig-name descname">pseudologlikelihood</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">data</span></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><p>Pseudo log likelihood of the probability distribution with respect to data</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>data</strong> – </p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.quantile">
<code class="sig-name descname">quantile</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">values</span></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><p>Return the Universe of Discourse values in relation to the quantile input values,
such that Q(tau) = min( {x | F(x) &gt;= tau })</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>values</strong> – input values</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>The list of the quantile values for the input values</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.set">
<code class="sig-name descname">set</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">value</span></em>, <em class="sig-param"><span class="n">density</span></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><p>Assert a probability ‘density’ for a certain value ‘value’, such that P(value) = density</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>value</strong> – A value in the universe of discourse from the distribution</p></li>
<li><p><strong>density</strong> – The probability density to assign to the value</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.type">
<code class="sig-name descname">type</code><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.type" title="Permalink to this definition"></a></dt>
<dd><p>If type is histogram, the PDF is discrete
If type is KDE the PDF is continuous</p>
</dd></dl>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.uod">
<code class="sig-name descname">uod</code><a class="headerlink" href="#pyFTS.probabilistic.ProbabilityDistribution.ProbabilityDistribution.uod" title="Permalink to this definition"></a></dt>
<dd><p>Universe of discourse</p>
</dd></dl>
</dd></dl>
<dl class="py function">
<dt id="pyFTS.probabilistic.ProbabilityDistribution.from_point">
<code class="sig-prename descclassname">pyFTS.probabilistic.ProbabilityDistribution.</code><code class="sig-name descname">from_point</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/ProbabilityDistribution.html#from_point"><span class="viewcode-link">[source]</span></a><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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – scalar value</p></li>
<li><p><strong>kwargs</strong> – common parameters of the distribution</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>the ProbabilityDistribution object</p>
</dd>
</dl>
</dd></dl>
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<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="py class">
<dt id="pyFTS.probabilistic.kde.KernelSmoothing">
<em class="property">class </em><code class="sig-prename descclassname">pyFTS.probabilistic.kde.</code><code class="sig-name descname">KernelSmoothing</code><span class="sig-paren">(</span><em class="sig-param"><span class="o">**</span><span class="n">kwargs</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/kde.html#KernelSmoothing"><span class="viewcode-link">[source]</span></a><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 v3.9)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Kernel Density Estimation</p>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.kde.KernelSmoothing.h">
<code class="sig-name descname">h</code><a class="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing.h" title="Permalink to this definition"></a></dt>
<dd><p>Width parameter</p>
</dd></dl>
<dl class="py attribute">
<dt id="pyFTS.probabilistic.kde.KernelSmoothing.kernel">
<code class="sig-name descname">kernel</code><a class="headerlink" href="#pyFTS.probabilistic.kde.KernelSmoothing.kernel" title="Permalink to this definition"></a></dt>
<dd><p>Kernel function</p>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.kde.KernelSmoothing.kernel_function">
<code class="sig-name descname">kernel_function</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">u</span></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><p>Apply the kernel</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>u</strong> – </p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt id="pyFTS.probabilistic.kde.KernelSmoothing.probability">
<code class="sig-name descname">probability</code><span class="sig-paren">(</span><em class="sig-param"><span class="n">x</span></em>, <em class="sig-param"><span class="o">**</span><span class="n">kwargs</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pyFTS/probabilistic/kde.html#KernelSmoothing.probability"><span class="viewcode-link">[source]</span></a><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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – </p></li>
<li><p><strong>data</strong> – </p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p></p>
</dd>
</dl>
</dd></dl>
</dd></dl>
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