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<section id="numpy-random-randomstate-vonmises">
<h1>numpy.random.RandomState.vonmises<a class="headerlink" href="#numpy-random-randomstate-vonmises" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.RandomState.vonmises">
<span class="sig-prename descclassname"><span class="pre">random.RandomState.</span></span><span class="sig-name descname"><span class="pre">vonmises</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kappa</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.vonmises" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a von Mises distribution.</p>
<p>Samples are drawn from a von Mises distribution with specified mode
(mu) and concentration (kappa), on the interval [-pi, pi].</p>
<p>The von Mises distribution (also known as the circular normal
distribution) is a continuous probability distribution on the unit
circle. It may be thought of as the circular analogue of the normal
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.vonmises.html#numpy.random.Generator.vonmises" title="numpy.random.Generator.vonmises"><code class="xref py py-obj docutils literal notranslate"><span class="pre">vonmises</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>mu</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Mode (“center”) of the distribution.</p>
</dd>
<dt><strong>kappa</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Concentration of the distribution, has to be >=0.</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">mu</span></code> and <code class="docutils literal notranslate"><span class="pre">kappa</span></code> are both scalars.
Otherwise, <code class="docutils literal notranslate"><span class="pre">np.broadcast(mu,</span> <span class="pre">kappa).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 von Mises distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html#scipy.stats.vonmises" title="(in SciPy v1.15.2)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.vonmises</span></code></a></dt><dd><p>probability density function, distribution, or cumulative density function, etc.</p>
</dd>
<dt><a class="reference internal" href="numpy.random.Generator.vonmises.html#numpy.random.Generator.vonmises" title="numpy.random.Generator.vonmises"><code class="xref py py-obj docutils literal notranslate"><span class="pre">random.Generator.vonmises</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 for the von Mises distribution is</p>
<div class="math notranslate nohighlight">
\[p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)},\]</div>
<p>where <span class="math notranslate nohighlight">\(\mu\)</span> is the mode and <span class="math notranslate nohighlight">\(\kappa\)</span> the concentration,
and <span class="math notranslate nohighlight">\(I_0(\kappa)\)</span> is the modified Bessel function of order 0.</p>
<p>The von Mises is named for Richard Edler von Mises, who was born in
Austria-Hungary, in what is now the Ukraine. He fled to the United
States in 1939 and became a professor at Harvard. He worked in
probability theory, aerodynamics, fluid mechanics, and philosophy of
science.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="r7ea57f32f5c1-1" 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="r7ea57f32f5c1-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>von Mises, R., “Mathematical Theory of Probability
and Statistics”, New York: Academic Press, 1964.</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">mu</span><span class="p">,</span> <span class="n">kappa</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">4.0</span> <span class="c1"># mean and concentration</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">vonmises</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">kappa</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="kn">from</span><span class="w"> </span><span class="nn">scipy.special</span><span class="w"> </span><span class="kn">import</span> <span class="n">i0</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">s</span><span class="p">,</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">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="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="mi">51</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</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="n">kappa</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="o">-</span><span class="n">mu</span><span class="p">))</span><span class="o">/</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="o">*</span><span class="n">i0</span><span class="p">(</span><span class="n">kappa</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">y</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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