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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution
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Parameters</a>
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</h3></div></div></div>
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<p>
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<a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">Random variates</a>
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and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution parameters</a>
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are conventionally distinguished (for example in Wikipedia and Wolfram MathWorld
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by placing a semi-colon after the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
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variate</a> (whose value you 'choose'), to separate the variate from
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the parameter(s) that defines the shape of the distribution.
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<p>
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For example, the binomial distribution has two parameters: n (the number
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of trials) and p (the probability of success on one trial). It also has the
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<a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
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<span class="emphasis"><em>k</em></span>: the number of successes observed. This means the
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probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k; n, p)</em></span>.
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</p>
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<p>
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Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
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constructor therefore has two parameters:
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</p>
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<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
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</pre>
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<p>
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While the function <code class="computeroutput"><span class="identifier">pdf</span></code> has
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one argument specifying the distribution type (which includes its parameters,
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if any), and a second argument for the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
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variate</a>. So taking our binomial distribution example, we would write:
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</p>
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<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial_distribution</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">);</span>
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</pre>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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