| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>Distributions are Objects</title> |
| <link rel="stylesheet" href="../../../math.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> |
| <link rel="home" href="../../../index.html" title="Math Toolkit 2.2.0"> |
| <link rel="up" href="../overview.html" title="Overview of Distributions"> |
| <link rel="prev" href="headers.html" title="Headers and Namespaces"> |
| <link rel="next" href="generic.html" title="Generic operations common to all distributions are non-member functions"> |
| </head> |
| <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> |
| <table cellpadding="2" width="100%"><tr> |
| <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> |
| <td align="center"><a href="../../../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../../../more/index.htm">More</a></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <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> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects">Distributions |
| are Objects</a> |
| </h4></div></div></div> |
| <p> |
| Each kind of distribution in this library is a class type - an object. |
| </p> |
| <p> |
| <a class="link" href="../../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policies</a> provide fine-grained control of |
| the behaviour of these classes, allowing the user to customise behaviour |
| such as how errors are handled, or how the quantiles of discrete distribtions |
| behave. |
| </p> |
| <div class="tip"><table border="0" summary="Tip"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../doc/src/images/tip.png"></td> |
| <th align="left">Tip</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| If you are familiar with statistics libraries using functions, and 'Distributions |
| as Objects' seem alien, see <a class="link" href="../weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the |
| comparison to other statistics libraries.</a> |
| </p></td></tr> |
| </table></div> |
| <p> |
| Making distributions class types does two things: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| It encapsulates the kind of distribution in the C++ type system; so, |
| for example, Students-t distributions are always a different C++ type |
| from Chi-Squared distributions. |
| </li> |
| <li class="listitem"> |
| The distribution objects store any parameters associated with the distribution: |
| for example, the Students-t distribution has a <span class="emphasis"><em>degrees of |
| freedom</em></span> parameter that controls the shape of the distribution. |
| This <span class="emphasis"><em>degrees of freedom</em></span> parameter has to be provided |
| to the Students-t object when it is constructed. |
| </li> |
| </ul></div> |
| <p> |
| Although the distribution classes in this library are templates, there |
| are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the usual |
| name of the distribution (except where there is a clash with a function |
| of the same name: beta and gamma, in which case using the default template |
| arguments - <code class="computeroutput"><span class="identifier">RealType</span> <span class="special">=</span> |
| <span class="keyword">double</span></code> - is nearly as convenient). |
| Probably 95% of uses are covered by these typedefs: |
| </p> |
| <pre class="programlisting"><span class="comment">// using namespace boost::math; // Avoid potential ambiguity with names in std <random></span> |
| <span class="comment">// Safer to declare specific functions with using statement(s):</span> |
| |
| <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> |
| <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> |
| <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> |
| |
| <span class="comment">// Construct a students_t distribution with 4 degrees of freedom:</span> |
| <span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| |
| <span class="comment">// Construct a double-precision beta distribution</span> |
| <span class="comment">// with parameters a = 10, b = 20</span> |
| <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> |
| </pre> |
| <p> |
| 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 |
| 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> |
| appended, for example: <a class="link" href="../../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students |
| t Distribution</a> or <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial |
| Distribution</a>: |
| </p> |
| <pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type,</span> |
| <span class="comment">// with 4 degrees of freedom:</span> |
| <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> |
| |
| <span class="comment">// Construct a binomial distribution, of long double type,</span> |
| <span class="comment">// with probability of success 0.3</span> |
| <span class="comment">// and 20 trials in total:</span> |
| <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> |
| </pre> |
| <p> |
| The parameters passed to the distributions can be accessed via getter member |
| functions: |
| </p> |
| <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> |
| </pre> |
| <p> |
| This is all well and good, but not very useful so far. What we often want |
| is to be able to calculate the <span class="emphasis"><em>cumulative distribution functions</em></span> |
| and <span class="emphasis"><em>quantiles</em></span> etc for these distributions. |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, |
| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| 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>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <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> |
| </div> |
| </body> |
| </html> |
