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<section id="numpy-random-generator-exponential">
<h1>numpy.random.Generator.exponential<a class="headerlink" href="#numpy-random-generator-exponential" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.Generator.exponential">
<span class="sig-prename descclassname"><span class="pre">random.Generator.</span></span><span class="sig-name descname"><span class="pre">exponential</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</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.Generator.exponential" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from an exponential distribution.</p>
<p>Its probability density function is</p>
<div class="math notranslate nohighlight">
\[f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),\]</div>
<p>for <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">></span> <span class="pre">0</span></code> and 0 elsewhere. <span class="math notranslate nohighlight">\(\beta\)</span> is the scale parameter,
which is the inverse of the rate parameter <span class="math notranslate nohighlight">\(\lambda = 1/\beta\)</span>.
The rate parameter is an alternative, widely used parameterization
of the exponential distribution <a class="reference internal" href="#r0dbb9b01ef9c-3" id="id1">[3]</a>.</p>
<p>The exponential distribution is a continuous analogue of the
geometric distribution. It describes many common situations, such as
the size of raindrops measured over many rainstorms <a class="reference internal" href="#r0dbb9b01ef9c-1" id="id2">[1]</a>, or the time
between page requests to Wikipedia <a class="reference internal" href="#r0dbb9b01ef9c-2" id="id3">[2]</a>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>scale</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>The scale parameter, <span class="math notranslate nohighlight">\(\beta = 1/\lambda\)</span>. 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">scale</span></code> is a scalar. Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(scale).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 exponential distribution.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r0dbb9b01ef9c-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id2">1</a><span class="fn-bracket">]</span></span>
<p>Peyton Z. Peebles Jr., “Probability, Random Variables and
Random Signal Principles”, 4th ed, 2001, p. 57.</p>
</div>
<div class="citation" id="r0dbb9b01ef9c-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id3">2</a><span class="fn-bracket">]</span></span>
<p>Wikipedia, “Poisson process”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Poisson_process">https://en.wikipedia.org/wiki/Poisson_process</a></p>
</div>
<div class="citation" id="r0dbb9b01ef9c-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">3</a><span class="fn-bracket">]</span></span>
<p>Wikipedia, “Exponential distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Exponential_distribution">https://en.wikipedia.org/wiki/Exponential_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="1911c7ca-d9a3-4548-85f7-3546d1700c6f">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('1911c7ca-d9a3-4548-85f7-3546d1700c6f','a2fc1997-95d5-4d1b-8c45-0cc1be66558e','fb3a43b0-e1c5-4c15-aa1a-40c84d59b526','../../../lite/tree/../notebooks/index.html?path=7af55115_b53f_4e80_be13_acc4ef0c26df.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<p>Assume a company has 10000 customer support agents and the time
between customer calls is exponentially distributed and that the
average time between customer calls is 4 minutes.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">scale</span><span class="p">,</span> <span class="n">size</span> <span class="o">=</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">10000</span>
<span class="gp">>>> </span><span class="n">rng</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">default_rng</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">time_between_calls</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">exponential</span><span class="p">(</span><span class="n">scale</span><span class="o">=</span><span class="n">scale</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</span>
</pre></div>
</div>
<p>What is the probability that a customer will call in the next
4 to 5 minutes?</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">((</span><span class="n">time_between_calls</span> <span class="o"><</span> <span class="mi">5</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">/</span><span class="n">size</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">((</span><span class="n">time_between_calls</span> <span class="o"><</span> <span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">/</span><span class="n">size</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">-</span> <span class="n">y</span>
<span class="go">0.08 # may vary</span>
</pre></div>
</div>
<p>The corresponding distribution can be visualized as follows:</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">scale</span><span class="p">,</span> <span class="n">size</span> <span class="o">=</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">10000</span>
<span class="gp">>>> </span><span class="n">rng</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">default_rng</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">sample</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">exponential</span><span class="p">(</span><span class="n">scale</span><span class="o">=</span><span class="n">scale</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">)</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">_</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">sample</span><span class="p">,</span> <span class="mi">30</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">bins</span><span class="p">,</span> <span class="n">scale</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">scale</span><span class="o">**-</span><span class="mi">1</span><span class="o">*</span><span class="n">bins</span><span class="p">),</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</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">show</span><span class="p">()</span>
</pre></div>
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