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26 <div class="titlepage"><div><div><h3 class="title">
27 <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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31 <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">Random variates</a>
32 and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution parameters</a>
33 are conventionally distinguished (for example in Wikipedia and Wolfram MathWorld
34 by placing a semi-colon after the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
35 variate</a> (whose value you 'choose'), to separate the variate from
36 the parameter(s) that defines the shape of the distribution.
39 For example, the binomial distribution has two parameters: n (the number
40 of trials) and p (the probability of success on one trial). It also has the
41 <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
42 <span class="emphasis"><em>k</em></span>: the number of successes observed. This means the
43 probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k; n, p)</em></span>.
46 Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
47 constructor therefore has two parameters:
49 <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>
52 While the function <code class="computeroutput"><span class="identifier">pdf</span></code> has
53 one argument specifying the distribution type (which includes its parameters,
54 if any), and a second argument for the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
55 variate</a>. So taking our binomial distribution example, we would write:
57 <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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