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<section id="numpy-random-randomstate-power">
<h1>numpy.random.RandomState.power<a class="headerlink" href="#numpy-random-randomstate-power" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.RandomState.power">
<span class="sig-prename descclassname"><span class="pre">random.RandomState.</span></span><span class="sig-name descname"><span class="pre">power</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.RandomState.power" title="Link to this definition">#</a></dt>
<dd><p>Draws samples in [0, 1] from a power distribution with positive
exponent a - 1.</p>
<p>Also known as the power function distribution.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <a class="reference internal" href="numpy.random.Generator.power.html#numpy.random.Generator.power" title="numpy.random.Generator.power"><code class="xref py py-obj docutils literal notranslate"><span class="pre">power</span></code></a>
method of a <a class="reference internal" href="../generator.html#numpy.random.Generator" title="numpy.random.Generator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator</span></code></a> instance instead;
please see the <a class="reference internal" href="../index.html#random-quick-start"><span class="std std-ref">Quick start</span></a>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>a</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Parameter of the distribution. Must be non-negative.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape. If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn. If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">a</span></code> is a scalar. Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(a).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized power distribution.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>ValueError</dt><dd><p>If a <= 0.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.random.Generator.power.html#numpy.random.Generator.power" title="numpy.random.Generator.power"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.power</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability density function is</p>
<div class="math notranslate nohighlight">
\[P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0.\]</div>
<p>The power function distribution is just the inverse of the Pareto
distribution. It may also be seen as a special case of the Beta
distribution.</p>
<p>It is used, for example, in modeling the over-reporting of insurance
claims.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="rc3722e0c6f7a-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Christian Kleiber, Samuel Kotz, “Statistical size distributions
in economics and actuarial sciences”, Wiley, 2003.</p>
</div>
<div class="citation" id="rc3722e0c6f7a-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Heckert, N. A. and Filliben, James J. “NIST Handbook 148:
Dataplot Reference Manual, Volume 2: Let Subcommands and Library
Functions”, National Institute of Standards and Technology
Handbook Series, June 2003.
<a class="reference external" href="https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf">https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf</a></p>
</div>
</div>
<p class="rubric">Examples</p>
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<p>Draw samples from the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="mf">5.</span> <span class="c1"># shape</span>
<span class="gp">>>> </span><span class="n">samples</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">samples</span><span class="p">)</span>
</pre></div>
</div>
<p>Display the histogram of the samples, along with
the probability density function:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="gp">>>> </span><span class="n">count</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">ignored</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="mf">1.</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">normed_y</span> <span class="o">=</span> <span class="n">samples</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">bins</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">y</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">normed_y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<figure class="align-default">
<img alt="../../../_images/numpy-random-RandomState-power-1_00_00.png" class="plot-directive" src="../../../_images/numpy-random-RandomState-power-1_00_00.png" />
</figure>
<p>Compare the power function distribution to the inverse of the Pareto.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">scipy</span><span class="w"> </span><span class="kn">import</span> <span class="n">stats</span>
<span class="gp">>>> </span><span class="n">rvs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">rvsp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">pareto</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">xx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">100</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">powpdf</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">powerlaw</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">rvs</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">powpdf</span><span class="p">,</span><span class="s1">'r-'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'np.random.power(5)'</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="mf">1.</span><span class="o">+</span><span class="n">rvsp</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">powpdf</span><span class="p">,</span><span class="s1">'r-'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'inverse of 1 + np.random.pareto(5)'</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="mf">1.</span><span class="o">/</span><span class="p">(</span><span class="mf">1.</span><span class="o">+</span><span class="n">rvsp</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span><span class="n">powpdf</span><span class="p">,</span><span class="s1">'r-'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">'inverse of stats.pareto(5)'</span><span class="p">)</span>
</pre></div>
</div>
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