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| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.dist.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters"> Random Variates |
| and Distribution Parameters</a> |
| </h4></div></div></div> |
| <p> |
| <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">Random variates</a> |
| and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution parameters</a> |
| are conventionally distinguished (for example in Wikipedia and Wolfram |
| MathWorld by placing a semi-colon after the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random |
| variate</a> (whose value you 'choose'), to separate the variate from |
| the parameter(s) that defines the shape of the distribution. |
| </p> |
| <p> |
| For example, the binomial distribution has two parameters: n (the number |
| of trials) and p (the probability of success on one trial). It also has |
| the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a> |
| <span class="emphasis"><em>k</em></span>: the number of successes observed. This means the |
| probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k; n, |
| p)</em></span>. |
| </p> |
| <p> |
| Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code> |
| constructor therefore has two parameters: |
| </p> |
| <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> |
| </pre> |
| <p> |
| While the function <code class="computeroutput"><span class="identifier">pdf</span></code> |
| has one argument specifying the distribution type (which includes it's |
| parameters, if any), and a second argument for the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random |
| variate</a>. So taking our binomial distribution example, we would |
| write: |
| </p> |
| <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> |
| </pre> |
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| Distributed under the Boost Software License, Version 1.0. (See accompanying |
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