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<div class="titlepage"><div><div><h4 class="title">
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<a name="math_toolkit.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects">Distributions
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are Objects</a>
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</h4></div></div></div>
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<p>
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Each kind of distribution in this library is a class type - an object,
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with member functions.
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</p>
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<div class="tip"><table border="0" summary="Tip">
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<tr>
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<th align="left">Tip</th>
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</tr>
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<tr><td align="left" valign="top"><p>
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If you are familiar with statistics libraries using functions, and 'Distributions
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as Objects' seem alien, see <a class="link" href="../weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the
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comparison to other statistics libraries.</a>
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</p></td></tr>
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</table></div>
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<p>
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<a class="link" href="../../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policies</a> provide optional fine-grained control
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of the behaviour of these classes, allowing the user to customise behaviour
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such as how errors are handled, or how the quantiles of discrete distributions
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behave.
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</p>
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<p>
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Making distributions class types does two things:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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It encapsulates the kind of distribution in the C++ type system; so,
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for example, Students-t distributions are always a different C++ type
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from Chi-Squared distributions.
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</li>
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<li class="listitem">
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The distribution objects store any parameters associated with the distribution:
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for example, the Students-t distribution has a <span class="emphasis"><em>degrees of
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freedom</em></span> parameter that controls the shape of the distribution.
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This <span class="emphasis"><em>degrees of freedom</em></span> parameter has to be provided
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to the Students-t object when it is constructed.
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</li>
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</ul></div>
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<p>
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Although the distribution classes in this library are templates, there
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are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the usual
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name of the distribution (except where there is a clash with a function
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of the same name: beta and gamma, in which case using the default template
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arguments - <code class="computeroutput"><span class="identifier">RealType</span> <span class="special">=</span>
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<span class="keyword">double</span></code> - is nearly as convenient).
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Probably 95% of uses are covered by these typedefs:
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</p>
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<pre class="programlisting"><span class="comment">// using namespace boost::math; // Avoid potential ambiguity with names in std <random></span>
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<span class="comment">// Safer to declare specific functions with using statement(s):</span>
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<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>
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<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>
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<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>
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<span class="comment">// Construct a students_t distribution with 4 degrees of freedom:</span>
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<span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>
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<span class="comment">// Construct a double-precision beta distribution</span>
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<span class="comment">// with parameters a = 10, b = 20</span>
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<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>
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</pre>
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<p>
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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
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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>
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appended, for example: <a class="link" href="../../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
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t Distribution</a> or <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
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Distribution</a>:
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</p>
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<pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type,</span>
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<span class="comment">// with 4 degrees of freedom:</span>
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<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>
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<span class="comment">// Construct a binomial distribution, of long double type,</span>
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<span class="comment">// with probability of success 0.3</span>
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<span class="comment">// and 20 trials in total:</span>
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<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>
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</pre>
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<p>
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The parameters passed to the distributions can be accessed via getter member
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functions:
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</p>
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<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>
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</pre>
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<p>
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This is all well and good, but not very useful so far. What we often want
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is to be able to calculate the <span class="emphasis"><em>cumulative distribution functions</em></span>
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and <span class="emphasis"><em>quantiles</em></span> etc for these distributions.
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</p>
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</div>
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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</p>
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