1/* boost random/student_t_distribution.hpp header file
2 *
3 * Copyright Steven Watanabe 2011
4 * Distributed under the Boost Software License, Version 1.0. (See
5 * accompanying file LICENSE_1_0.txt or copy at
6 * http://www.boost.org/LICENSE_1_0.txt)
7 *
8 * See http://www.boost.org for most recent version including documentation.
9 *
10 * $Id$
11 */
12
13#ifndef BOOST_RANDOM_STUDENT_T_DISTRIBUTION_HPP
14#define BOOST_RANDOM_STUDENT_T_DISTRIBUTION_HPP
15
16#include <boost/config/no_tr1/cmath.hpp>
17#include <iosfwd>
18#include <boost/config.hpp>
19#include <boost/limits.hpp>
20#include <boost/random/detail/operators.hpp>
21#include <boost/random/chi_squared_distribution.hpp>
22#include <boost/random/normal_distribution.hpp>
23
24namespace boost {
25namespace random {
26
27/**
28 * The Student t distribution is a real valued distribution with one
29 * parameter n, the number of degrees of freedom.
30 *
31 * It has \f$\displaystyle p(x) =
32 * \frac{1}{\sqrt{n\pi}}
33 * \frac{\Gamma((n+1)/2)}{\Gamma(n/2)}
34 * \left(1+\frac{x^2}{n}\right)^{-(n+1)/2}
35 * \f$.
36 */
37template<class RealType = double>
38class student_t_distribution {
39public:
40 typedef RealType result_type;
41 typedef RealType input_type;
42
43 class param_type {
44 public:
45 typedef student_t_distribution distribution_type;
46
47 /**
48 * Constructs a @c param_type with "n" degrees of freedom.
49 *
50 * Requires: n > 0
51 */
52 explicit param_type(RealType n_arg = RealType(1.0))
53 : _n(n_arg)
54 {}
55
56 /** Returns the number of degrees of freedom of the distribution. */
57 RealType n() const { return _n; }
58
59 /** Writes a @c param_type to a @c std::ostream. */
60 BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
61 { os << parm._n; return os; }
62
63 /** Reads a @c param_type from a @c std::istream. */
64 BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
65 { is >> parm._n; return is; }
66
67 /** Returns true if the two sets of parameters are the same. */
68 BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
69 { return lhs._n == rhs._n; }
70
71 /** Returns true if the two sets of parameters are the different. */
72 BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
73
74 private:
75 RealType _n;
76 };
77
78 /**
79 * Constructs an @c student_t_distribution with "n" degrees of freedom.
80 *
81 * Requires: n > 0
82 */
83 explicit student_t_distribution(RealType n_arg = RealType(1.0))
84 : _normal(), _chi_squared(n_arg)
85 {}
86 /** Constructs an @c student_t_distribution from its parameters. */
87 explicit student_t_distribution(const param_type& parm)
88 : _normal(), _chi_squared(parm.n())
89 {}
90
91 /**
92 * Returns a random variate distributed according to the
93 * Student t distribution.
94 */
95 template<class URNG>
96 RealType operator()(URNG& urng)
97 {
98 using std::sqrt;
99 return _normal(urng) / sqrt(_chi_squared(urng) / n());
100 }
101
102 /**
103 * Returns a random variate distributed accordint to the Student
104 * t distribution with parameters specified by @c param.
105 */
106 template<class URNG>
107 RealType operator()(URNG& urng, const param_type& parm) const
108 {
109 return student_t_distribution(parm)(urng);
110 }
111
112 /** Returns the number of degrees of freedom. */
113 RealType n() const { return _chi_squared.n(); }
114
115 /** Returns the smallest value that the distribution can produce. */
116 RealType min BOOST_PREVENT_MACRO_SUBSTITUTION () const
117 { return -std::numeric_limits<RealType>::infinity(); }
118 /** Returns the largest value that the distribution can produce. */
119 RealType max BOOST_PREVENT_MACRO_SUBSTITUTION () const
120 { return std::numeric_limits<RealType>::infinity(); }
121
122 /** Returns the parameters of the distribution. */
123 param_type param() const { return param_type(n()); }
124 /** Sets the parameters of the distribution. */
125 void param(const param_type& parm)
126 {
127 typedef chi_squared_distribution<RealType> chi_squared_type;
128 typename chi_squared_type::param_type chi_squared_param(parm.n());
129 _chi_squared.param(chi_squared_param);
130 }
131
132 /**
133 * Effects: Subsequent uses of the distribution do not depend
134 * on values produced by any engine prior to invoking reset.
135 */
136 void reset()
137 {
138 _normal.reset();
139 _chi_squared.reset();
140 }
141
142 /** Writes a @c student_t_distribution to a @c std::ostream. */
143 BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, student_t_distribution, td)
144 {
145 os << td.param();
146 return os;
147 }
148
149 /** Reads a @c student_t_distribution from a @c std::istream. */
150 BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, student_t_distribution, td)
151 {
152 param_type parm;
153 if(is >> parm) {
154 td.param(parm);
155 }
156 return is;
157 }
158
159 /**
160 * Returns true if the two instances of @c student_t_distribution will
161 * return identical sequences of values given equal generators.
162 */
163 BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(student_t_distribution, lhs, rhs)
164 { return lhs._normal == rhs._normal && lhs._chi_squared == rhs._chi_squared; }
165
166 /**
167 * Returns true if the two instances of @c student_t_distribution will
168 * return different sequences of values given equal generators.
169 */
170 BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(student_t_distribution)
171
172private:
173 normal_distribution<RealType> _normal;
174 chi_squared_distribution<RealType> _chi_squared;
175};
176
177} // namespace random
178} // namespace boost
179
180#endif // BOOST_RANDOM_STUDENT_T_DISTRIBUTION_HPP
181