1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Random Variates and Distribution Parameters</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../stat_tut.html" title="Statistical Distributions Tutorial"> 9<link rel="prev" href="weg/c_sharp.html" title="Using the Distributions from Within C#"> 10<link rel="next" href="dist_params.html" title="Discrete Probability Distributions"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="weg/c_sharp.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dist_params.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 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 28 Parameters</a> 29</h3></div></div></div> 30<p> 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. 37 </p> 38<p> 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>. 44 </p> 45<p> 46 Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code> 47 constructor therefore has two parameters: 48 </p> 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> 50</pre> 51<p> 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: 56 </p> 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> 58</pre> 59</div> 60<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 61<td align="left"></td> 62<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 63 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 64 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 65 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 66 Daryle Walker and Xiaogang Zhang<p> 67 Distributed under the Boost Software License, Version 1.0. (See accompanying 68 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 69 </p> 70</div></td> 71</tr></table> 72<hr> 73<div class="spirit-nav"> 74<a accesskey="p" href="weg/c_sharp.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../stat_tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dist_params.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 75</div> 76</body> 77</html> 78
