1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Distributions are Objects</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="../overview.html" title="Overview of Statistical Distributions"> 9<link rel="prev" href="headers.html" title="Headers and Namespaces"> 10<link rel="next" href="generic.html" title="Generic operations common to all distributions are non-member functions"> 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="headers.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.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="generic.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h4 class="title"> 27<a name="math_toolkit.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects">Distributions 28 are Objects</a> 29</h4></div></div></div> 30<p> 31 Each kind of distribution in this library is a class type - an object, 32 with member functions. 33 </p> 34<div class="tip"><table border="0" summary="Tip"> 35<tr> 36<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../doc/src/images/tip.png"></td> 37<th align="left">Tip</th> 38</tr> 39<tr><td align="left" valign="top"><p> 40 If you are familiar with statistics libraries using functions, and 'Distributions 41 as Objects' seem alien, see <a class="link" href="../weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the 42 comparison to other statistics libraries.</a> 43 </p></td></tr> 44</table></div> 45<p> 46 <a class="link" href="../../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policies</a> provide optional fine-grained control 47 of the behaviour of these classes, allowing the user to customise behaviour 48 such as how errors are handled, or how the quantiles of discrete distributions 49 behave. 50 </p> 51<p> 52 Making distributions class types does two things: 53 </p> 54<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 55<li class="listitem"> 56 It encapsulates the kind of distribution in the C++ type system; so, 57 for example, Students-t distributions are always a different C++ type 58 from Chi-Squared distributions. 59 </li> 60<li class="listitem"> 61 The distribution objects store any parameters associated with the distribution: 62 for example, the Students-t distribution has a <span class="emphasis"><em>degrees of 63 freedom</em></span> parameter that controls the shape of the distribution. 64 This <span class="emphasis"><em>degrees of freedom</em></span> parameter has to be provided 65 to the Students-t object when it is constructed. 66 </li> 67</ul></div> 68<p> 69 Although the distribution classes in this library are templates, there 70 are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the usual 71 name of the distribution (except where there is a clash with a function 72 of the same name: beta and gamma, in which case using the default template 73 arguments - <code class="computeroutput"><span class="identifier">RealType</span> <span class="special">=</span> 74 <span class="keyword">double</span></code> - is nearly as convenient). 75 Probably 95% of uses are covered by these typedefs: 76 </p> 77<pre class="programlisting"><span class="comment">// using namespace boost::math; // Avoid potential ambiguity with names in std <random></span> 78<span class="comment">// Safer to declare specific functions with using statement(s):</span> 79 80<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta_distribution</span><span class="special">;</span> 81<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial_distribution</span><span class="special">;</span> 82<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">students_t</span><span class="special">;</span> 83 84<span class="comment">// Construct a students_t distribution with 4 degrees of freedom:</span> 85<span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> 86 87<span class="comment">// Construct a double-precision beta distribution</span> 88<span class="comment">// with parameters a = 10, b = 20</span> 89<span class="identifier">beta_distribution</span><span class="special"><></span> <span class="identifier">d2</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> <span class="comment">// Note: _distribution<> suffix !</span> 90</pre> 91<p> 92 If you need to use the distributions with a type other than <code class="computeroutput"><span class="keyword">double</span></code>, then you can instantiate the template 93 directly: the names of the templates are the same as the <code class="computeroutput"><span class="keyword">double</span></code> typedef but with <code class="computeroutput"><span class="identifier">_distribution</span></code> 94 appended, for example: <a class="link" href="../../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students 95 t Distribution</a> or <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial 96 Distribution</a>: 97 </p> 98<pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type,</span> 99<span class="comment">// with 4 degrees of freedom:</span> 100<span class="identifier">students_t_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">d3</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> 101 102<span class="comment">// Construct a binomial distribution, of long double type,</span> 103<span class="comment">// with probability of success 0.3</span> 104<span class="comment">// and 20 trials in total:</span> 105<span class="identifier">binomial_distribution</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">d4</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">);</span> 106</pre> 107<p> 108 The parameters passed to the distributions can be accessed via getter member 109 functions: 110 </p> 111<pre class="programlisting"><span class="identifier">d1</span><span class="special">.</span><span class="identifier">degrees_of_freedom</span><span class="special">();</span> <span class="comment">// returns 4.0</span> 112</pre> 113<p> 114 This is all well and good, but not very useful so far. What we often want 115 is to be able to calculate the <span class="emphasis"><em>cumulative distribution functions</em></span> 116 and <span class="emphasis"><em>quantiles</em></span> etc for these distributions. 117 </p> 118</div> 119<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 120<td align="left"></td> 121<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 122 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 123 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 124 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 125 Daryle Walker and Xiaogang Zhang<p> 126 Distributed under the Boost Software License, Version 1.0. (See accompanying 127 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>) 128 </p> 129</div></td> 130</tr></table> 131<hr> 132<div class="spirit-nav"> 133<a accesskey="p" href="headers.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../overview.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="generic.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 134</div> 135</body> 136</html> 137
