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<section id="numpy-random-randomstate-laplace">
<h1>numpy.random.RandomState.laplace<a class="headerlink" href="#numpy-random-randomstate-laplace" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.RandomState.laplace">
<span class="sig-prename descclassname"><span class="pre">random.RandomState.</span></span><span class="sig-name descname"><span class="pre">laplace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">loc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <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.RandomState.laplace" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from the Laplace or double exponential distribution with
specified location (or mean) and scale (decay).</p>
<p>The Laplace distribution is similar to the Gaussian/normal distribution,
but is sharper at the peak and has fatter tails. It represents the
difference between two independent, identically distributed exponential
random variables.</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.laplace.html#numpy.random.Generator.laplace" title="numpy.random.Generator.laplace"><code class="xref py py-obj docutils literal notranslate"><span class="pre">laplace</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>loc</strong><span class="classifier">float or array_like of floats, optional</span></dt><dd><p>The position, <span class="math notranslate nohighlight">\(\mu\)</span>, of the distribution peak. Default is 0.</p>
</dd>
<dt><strong>scale</strong><span class="classifier">float or array_like of floats, optional</span></dt><dd><p><span class="math notranslate nohighlight">\(\lambda\)</span>, the exponential decay. Default is 1. 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">loc</span></code> and <code class="docutils literal notranslate"><span class="pre">scale</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(loc,</span> <span class="pre">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 Laplace distribution.</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.laplace.html#numpy.random.Generator.laplace" title="numpy.random.Generator.laplace"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.laplace</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>It has the probability density function</p>
<div class="math notranslate nohighlight">
\[f(x; \mu, \lambda) = \frac{1}{2\lambda}
\exp\left(-\frac{|x - \mu|}{\lambda}\right).\]</div>
<p>The first law of Laplace, from 1774, states that the frequency
of an error can be expressed as an exponential function of the
absolute magnitude of the error, which leads to the Laplace
distribution. For many problems in economics and health
sciences, this distribution seems to model the data better
than the standard Gaussian distribution.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r3d00038c3802-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>Abramowitz, M. and Stegun, I. A. (Eds.). “Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical
Tables, 9th printing,” New York: Dover, 1972.</p>
</div>
<div class="citation" id="r3d00038c3802-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Kotz, Samuel, et. al. “The Laplace Distribution and
Generalizations, “ Birkhauser, 2001.</p>
</div>
<div class="citation" id="r3d00038c3802-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
<p>Weisstein, Eric W. “Laplace Distribution.”
From MathWorld–A Wolfram Web Resource.
<a class="reference external" href="https://mathworld.wolfram.com/LaplaceDistribution.html">https://mathworld.wolfram.com/LaplaceDistribution.html</a></p>
</div>
<div class="citation" id="r3d00038c3802-4" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>4<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Laplace distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Laplace_distribution">https://en.wikipedia.org/wiki/Laplace_distribution</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">loc</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</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">laplace</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">scale</span><span class="p">,</span> <span class="mi">1000</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="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">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">8.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">.01</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pdf</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="nb">abs</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">loc</span><span class="p">)</span><span class="o">/</span><span class="n">scale</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span><span class="o">*</span><span class="n">scale</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">x</span><span class="p">,</span> <span class="n">pdf</span><span class="p">)</span>
</pre></div>
</div>
<p>Plot Gaussian for comparison:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">g</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="p">(</span><span class="n">scale</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> <span class="o">*</span>
<span class="gp">... </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="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">loc</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">scale</span><span class="o">**</span><span class="mi">2</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">x</span><span class="p">,</span><span class="n">g</span><span class="p">)</span>
</pre></div>
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