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jorenham committed Dec 13, 2023
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</span>
</a>

</li>

<li class="md-nav__item">
<a href="#lmo.distributions.genlambda" class="md-nav__link">
<span class="md-ellipsis">
genlambda
</span>
</a>

</li>

<li class="md-nav__item">
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</ul>
</nav>

</li>

<li class="md-nav__item">
<a href="#lmo.distributions.wakeby_gen" class="md-nav__link">
<span class="md-ellipsis">
wakeby_gen
</span>
</a>

</li>

</ul>
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</span>
</a>

</li>

<li class="md-nav__item">
<a href="#lmo.theoretical.entropy_from_qdf" class="md-nav__link">
<span class="md-ellipsis">
entropy_from_qdf()
</span>
</a>

</li>

</ul>
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<p>A Wakeby random variable, a generalization of
<a class="autorefs autorefs-external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto"><code>scipy.stats.genpareto</code></a>.</p>
<p><a class="autorefs autorefs-internal" href="../distributions/#wakeby"><code>wakeby</code></a> takes <span class="arithmatex">\( b \)</span>, <span class="arithmatex">\( d \)</span> and <span class="arithmatex">\( f \)</span> as shape parameters.</p>
<p>For details, see <a href="../distributions/#wakeby">Theoretical L-moments - Wakeby</a>.</p>
<p>For a detailed description of the Wakeby distribution, refer to
<a href="../distributions/#wakeby">Distributions - Wakeby</a>.</p>
</div>

</div>

<div class="doc doc-object doc-attribute">




<h4 id="lmo.distributions.genlambda" class="doc doc-heading">
<code class="highlight language-python"><span class="n">lmo</span><span class="o">.</span><span class="n">distributions</span><span class="o">.</span><span class="n">genlambda</span><span class="p">:</span> <span class="n">RVContinuous</span><span class="p">[</span><span class="nb">float</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">float</span><span class="p">]</span> <span class="o">=</span> <span class="n">genlambda_gen</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">&#39;genlambda&#39;</span><span class="p">)</span></code>

<span class="doc doc-labels">
<small class="doc doc-label doc-label-module-attribute"><code>module-attribute</code></small>
</span>

<a href="#lmo.distributions.genlambda" class="headerlink" title="Permanent link">&para;</a></h4>


<div class="doc doc-contents ">

<p>A generalized Tukey-Lambda random variable.</p>
<p><code>genlambda</code> takes <code>b</code>, <code>d</code> and <code>f</code> as shape parameters.
<code>b</code> and <code>d</code> can be any float, and <code>f</code> requires <code>-1 &lt;= f &lt;= 1</code>.</p>
<p>If <code>f == 0</code> and <code>b == d</code>, <code>genlambda</code> is equivalent to
<a class="autorefs autorefs-external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tukeylambda.html#scipy.stats.tukeylambda"><code>scipy.stats.tukeylambda</code></a>, with <code>b</code> (or <code>d</code>) as
shape parameter.</p>
<p>For a detailed description of the GLD, refer to
<a href="../distributions/#gld">Distributions - GLD</a>.</p>
</div>

</div>
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</div>

</div>

</div>

<div class="doc doc-object doc-class">




<h4 id="lmo.distributions.wakeby_gen" class="doc doc-heading">
<code>lmo.distributions.wakeby_gen</code>


<a href="#lmo.distributions.wakeby_gen" class="headerlink" title="Permanent link">&para;</a></h4>


<div class="doc doc-contents ">
<p class="doc doc-class-bases">
Bases: <code><span title="scipy.stats.distributions.rv_continuous">_rv_continuous</span></code></p>





<div class="doc doc-children">











</div>

</div>
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</div>


<div class="doc doc-object doc-function">




<h4 id="lmo.theoretical.entropy_from_qdf" class="doc doc-heading">
<code class="highlight language-python"><span class="n">lmo</span><span class="o">.</span><span class="n">theoretical</span><span class="o">.</span><span class="n">entropy_from_qdf</span><span class="p">(</span><span class="n">qdf</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span></code>

<a href="#lmo.theoretical.entropy_from_qdf" class="headerlink" title="Permanent link">&para;</a></h4>


<div class="doc doc-contents ">

<p>Evaluate the (differential / continuous) entropy <span class="arithmatex">\( H(X) \)</span> of a
univariate random variable <span class="arithmatex">\( X \)</span>, from its <em>quantile density
function</em> (QDF), <span class="arithmatex">\( q(u) = \frac{\mathrm{d} F^{-1}(u)}{\mathrm{d} u} \)</span>,
with <span class="arithmatex">\( F^{-1} \)</span> the inverse of the CDF, i.e. the PPF / quantile function.</p>
<p>The derivation follows from the identity <span class="arithmatex">\( f(x) = 1 / q(F(x)) \)</span> of PDF
<span class="arithmatex">\( f \)</span>, specifically:</p>
<div class="arithmatex">\[
h(X)
= \E[-\ln f(X)]
= \int_\mathbb{R} \ln \frac{1}{f(x)} \mathrm{d} x
= \int_1 \ln q(u) \mathrm{d} u
\]</div>



<table>
<thead>
<tr>
<th><b>PARAMETER</b></th>
<th><b> DESCRIPTION</b></th>
</tr>
</thead>
<tbody>
<tr>
<td><code>qdf</code></td>
<td class="doc-param-details">
<div class="doc-md-description">
<p>The quantile distribution function (QDF).</p>
</div>
<p>
<span class="doc-param-annotation">
<b>TYPE:</b>
<code> (float, *Ts, **Ts) -&gt; float</code>
</span>
</p>
</td>
</tr>
<tr>
<td><code>*args</code></td>
<td class="doc-param-details">
<div class="doc-md-description">
<p>Optional additional positional arguments to pass to <code>qdf</code>.</p>
</div>
<p>
<span class="doc-param-annotation">
<b>TYPE:</b>
<code>*Ts</code>
</span>
<span class="doc-param-default">
<b>DEFAULT:</b>
<code>()</code>
</span>
</p>
</td>
</tr>
<tr>
<td><code>**kwds</code></td>
<td class="doc-param-details">
<div class="doc-md-description">
<p>Optional keyword arguments to pass to <code>qdf</code>.</p>
</div>
<p>
<span class="doc-param-annotation">
<b>TYPE:</b>
<code>**Ts</code>
</span>
<span class="doc-param-default">
<b>DEFAULT:</b>
<code>{}</code>
</span>
</p>
</td>
</tr>
</tbody>
</table>



<table>
<thead>
<tr>
<th><b>RETURNS</b></th>
<th><b>DESCRIPTION</b></th>
</tr>
</thead>
<tbody>
<tr>
<td>
<span class="doc-returns-annotation">
<code><a class="autorefs autorefs-external" href="https://docs.python.org/3/library/functions.html#float">float</a></code>
</span>
</td>
<td class="doc-returns-details">
<div class="doc-md-description">
<p>The differential entropy <span class="arithmatex">\( h(X) \)</span>.</p>
</div>
</td>
</tr>
</tbody>
</table>

<details class="see-also" open>
<summary>See Also</summary>
<ul>
<li><a href="https://wikipedia.org/wiki/Differential_entropy">Differential entropy - Wikipedia
</a></li>
</ul>
</details>
</div>

</div>



</div>

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</div>


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