1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
|
/* boost random/negative_binomial_distribution.hpp header file
*
* Copyright Steven Watanabe 2010
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* See http://www.boost.org for most recent version including documentation.
*
* $Id: negative_binomial_distribution.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
*/
#ifndef BOOST_RANDOM_NEGATIVE_BINOMIAL_DISTRIBUTION_HPP_INCLUDED
#define BOOST_RANDOM_NEGATIVE_BINOMIAL_DISTRIBUTION_HPP_INCLUDED
#include <iosfwd>
#include <boost/limits.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/poisson_distribution.hpp>
namespace boost {
namespace random {
/**
* The negative binomial distribution is an integer valued
* distribution with two parameters, @c k and @c p. The
* distribution produces non-negative values.
*
* The distribution function is
* \f$\displaystyle P(i) = {k+i-1\choose i}p^k(1-p)^i\f$.
*
* This implementation uses a gamma-poisson mixture.
*/
template<class IntType = int, class RealType = double>
class negative_binomial_distribution {
public:
typedef IntType result_type;
typedef RealType input_type;
class param_type {
public:
typedef negative_binomial_distribution distribution_type;
/**
* Construct a param_type object. @c k and @c p
* are the parameters of the distribution.
*
* Requires: k >=0 && 0 <= p <= 1
*/
explicit param_type(IntType k_arg = 1, RealType p_arg = RealType (0.5))
: _k(k_arg), _p(p_arg)
{}
/** Returns the @c k parameter of the distribution. */
IntType k() const { return _k; }
/** Returns the @c p parameter of the distribution. */
RealType p() const { return _p; }
#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
/** Writes the parameters of the distribution to a @c std::ostream. */
template<class CharT, class Traits>
friend std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>& os,
const param_type& parm)
{
os << parm._p << " " << parm._k;
return os;
}
/** Reads the parameters of the distribution from a @c std::istream. */
template<class CharT, class Traits>
friend std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& is, param_type& parm)
{
is >> parm._p >> std::ws >> parm._k;
return is;
}
#endif
/** Returns true if the parameters have the same values. */
friend bool operator==(const param_type& lhs, const param_type& rhs)
{
return lhs._k == rhs._k && lhs._p == rhs._p;
}
/** Returns true if the parameters have different values. */
friend bool operator!=(const param_type& lhs, const param_type& rhs)
{
return !(lhs == rhs);
}
private:
IntType _k;
RealType _p;
};
/**
* Construct a @c negative_binomial_distribution object. @c k and @c p
* are the parameters of the distribution.
*
* Requires: k >=0 && 0 <= p <= 1
*/
explicit negative_binomial_distribution(IntType k_arg = 1,
RealType p_arg = RealType(0.5))
: _k(k_arg), _p(p_arg)
{}
/**
* Construct an @c negative_binomial_distribution object from the
* parameters.
*/
explicit negative_binomial_distribution(const param_type& parm)
: _k(parm.k()), _p(parm.p())
{}
/**
* Returns a random variate distributed according to the
* negative binomial distribution.
*/
template<class URNG>
IntType operator()(URNG& urng) const
{
gamma_distribution<RealType> gamma(_k, (1-_p)/_p);
poisson_distribution<IntType, RealType> poisson(gamma(urng));
return poisson(urng);
}
/**
* Returns a random variate distributed according to the negative
* binomial distribution with parameters specified by @c param.
*/
template<class URNG>
IntType operator()(URNG& urng, const param_type& parm) const
{
return negative_binomial_distribution(parm)(urng);
}
/** Returns the @c k parameter of the distribution. */
IntType k() const { return _k; }
/** Returns the @c p parameter of the distribution. */
RealType p() const { return _p; }
/** Returns the smallest value that the distribution can produce. */
IntType min BOOST_PREVENT_MACRO_SUBSTITUTION() const { return 0; }
/** Returns the largest value that the distribution can produce. */
IntType max BOOST_PREVENT_MACRO_SUBSTITUTION() const
{ return (std::numeric_limits<IntType>::max)(); }
/** Returns the parameters of the distribution. */
param_type param() const { return param_type(_k, _p); }
/** Sets parameters of the distribution. */
void param(const param_type& parm)
{
_k = parm.k();
_p = parm.p();
}
/**
* Effects: Subsequent uses of the distribution do not depend
* on values produced by any engine prior to invoking reset.
*/
void reset() { }
#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
/** Writes the parameters of the distribution to a @c std::ostream. */
template<class CharT, class Traits>
friend std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>& os,
const negative_binomial_distribution& bd)
{
os << bd.param();
return os;
}
/** Reads the parameters of the distribution from a @c std::istream. */
template<class CharT, class Traits>
friend std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& is,
negative_binomial_distribution& bd)
{
bd.read(is);
return is;
}
#endif
/** Returns true if the two distributions will produce the same
sequence of values, given equal generators. */
friend bool operator==(const negative_binomial_distribution& lhs,
const negative_binomial_distribution& rhs)
{
return lhs._k == rhs._k && lhs._p == rhs._p;
}
/** Returns true if the two distributions could produce different
sequences of values, given equal generators. */
friend bool operator!=(const negative_binomial_distribution& lhs,
const negative_binomial_distribution& rhs)
{
return !(lhs == rhs);
}
private:
/// @cond \show_private
template<class CharT, class Traits>
void read(std::basic_istream<CharT, Traits>& is) {
param_type parm;
if(is >> parm) {
param(parm);
}
}
// parameters
IntType _k;
RealType _p;
/// @endcond
};
}
}
#endif
|
