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26 <div class=
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"title">
27 <a name=
"math_toolkit.stat_tut.overview.objects"></a><a class=
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"Distributions are Objects">Distributions
29 </h4></div></div></div>
31 Each kind of distribution in this library is a class type - an object.
34 <a class=
"link" href=
"../../../policy.html" title=
"Chapter 15. Policies: Controlling Precision, Error Handling etc">Policies
</a> provide fine-grained control of
35 the behaviour of these classes, allowing the user to customise behaviour
36 such as how errors are handled, or how the quantiles of discrete distribtions
39 <div class=
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42 <th align=
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44 <tr><td align=
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45 If you are familiar with statistics libraries using functions, and 'Distributions
46 as Objects' seem alien, see
<a class=
"link" href=
"../weg/nag_library.html" title=
"Comparison with C, R, FORTRAN-style Free Functions">the
47 comparison to other statistics libraries.
</a>
51 Making distributions class types does two things:
53 <div class=
"itemizedlist"><ul class=
"itemizedlist" style=
"list-style-type: disc; ">
55 It encapsulates the kind of distribution in the C++ type system; so,
56 for example, Students-t distributions are always a different C++ type
57 from Chi-Squared distributions.
60 The distribution objects store any parameters associated with the distribution:
61 for example, the Students-t distribution has a
<span class=
"emphasis"><em>degrees of
62 freedom
</em></span> parameter that controls the shape of the distribution.
63 This
<span class=
"emphasis"><em>degrees of freedom
</em></span> parameter has to be provided
64 to the Students-t object when it is constructed.
68 Although the distribution classes in this library are templates, there
69 are typedefs on type
<span class=
"emphasis"><em>double
</em></span> that mostly take the usual
70 name of the distribution (except where there is a clash with a function
71 of the same name: beta and gamma, in which case using the default template
72 arguments -
<code class=
"computeroutput"><span class=
"identifier">RealType
</span> <span class=
"special">=
</span>
73 <span class=
"keyword">double
</span></code> - is nearly as convenient).
74 Probably
95% of uses are covered by these typedefs:
76 <pre class=
"programlisting"><span class=
"comment">// using namespace boost::math; // Avoid potential ambiguity with names in std
<random
></span>
77 <span class=
"comment">// Safer to declare specific functions with using statement(s):
</span>
79 <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>
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">binomial_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">students_t
</span><span class=
"special">;
</span>
83 <span class=
"comment">// Construct a students_t distribution with
4 degrees of freedom:
</span>
84 <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 <span class=
"comment">// Construct a double-precision beta distribution
</span>
87 <span class=
"comment">// with parameters a =
10, b =
20</span>
88 <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>
91 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
92 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>
93 appended, for example:
<a class=
"link" href=
"../../dist_ref/dists/students_t_dist.html" title=
"Students t Distribution">Students
94 t Distribution
</a> or
<a class=
"link" href=
"../../dist_ref/dists/binomial_dist.html" title=
"Binomial Distribution">Binomial
97 <pre class=
"programlisting"><span class=
"comment">// Construct a students_t distribution, of float type,
</span>
98 <span class=
"comment">// with
4 degrees of freedom:
</span>
99 <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 <span class=
"comment">// Construct a binomial distribution, of long double type,
</span>
102 <span class=
"comment">// with probability of success
0.3</span>
103 <span class=
"comment">// and
20 trials in total:
</span>
104 <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>
107 The parameters passed to the distributions can be accessed via getter member
110 <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>
113 This is all well and good, but not very useful so far. What we often want
114 is to be able to calculate the
<span class=
"emphasis"><em>cumulative distribution functions
</em></span>
115 and
<span class=
"emphasis"><em>quantiles
</em></span> etc for these distributions.
118 <table xmlns:
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119 <td align=
"left"></td>
120 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
121 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
122 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
123 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
124 Distributed under the Boost Software License, Version
1.0. (See accompanying
125 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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