1// Copyright John Maddock 2006.
2
3// Use, modification and distribution are subject to the
4// Boost Software License, Version 1.0.
5// (See accompanying file LICENSE_1_0.txt
6// or copy at http://www.boost.org/LICENSE_1_0.txt)
7
8#ifndef BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
9#define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
10
11#include <boost/math/distributions/fwd.hpp>
12#include <boost/math/special_functions/beta.hpp> // for incomplete beta.
13#include <boost/math/distributions/complement.hpp> // complements
14#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
15#include <boost/math/special_functions/fpclassify.hpp>
16
17#include <utility>
18
19namespace boost{ namespace math{
20
21template <class RealType = double, class Policy = policies::policy<> >
22class fisher_f_distribution
23{
24public:
25 typedef RealType value_type;
26 typedef Policy policy_type;
27
28 fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j)
29 {
30 static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution";
31 RealType result;
32 detail::check_df(
33 function, m_df1, &result, Policy());
34 detail::check_df(
35 function, m_df2, &result, Policy());
36 } // fisher_f_distribution
37
38 RealType degrees_of_freedom1()const
39 {
40 return m_df1;
41 }
42 RealType degrees_of_freedom2()const
43 {
44 return m_df2;
45 }
46
47private:
48 //
49 // Data members:
50 //
51 RealType m_df1; // degrees of freedom are a real number.
52 RealType m_df2; // degrees of freedom are a real number.
53};
54
55typedef fisher_f_distribution<double> fisher_f;
56
57#ifdef __cpp_deduction_guides
58template <class RealType>
59fisher_f_distribution(RealType,RealType)->fisher_f_distribution<typename boost::math::tools::promote_args<RealType>::type>;
60#endif
61
62template <class RealType, class Policy>
63inline const std::pair<RealType, RealType> range(const fisher_f_distribution<RealType, Policy>& /*dist*/)
64{ // Range of permissible values for random variable x.
65 using boost::math::tools::max_value;
66 return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
67}
68
69template <class RealType, class Policy>
70inline const std::pair<RealType, RealType> support(const fisher_f_distribution<RealType, Policy>& /*dist*/)
71{ // Range of supported values for random variable x.
72 // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
73 using boost::math::tools::max_value;
74 return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
75}
76
77template <class RealType, class Policy>
78RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
79{
80 BOOST_MATH_STD_USING // for ADL of std functions
81 RealType df1 = dist.degrees_of_freedom1();
82 RealType df2 = dist.degrees_of_freedom2();
83 // Error check:
84 RealType error_result = 0;
85 static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)";
86 if(false == (detail::check_df(
87 function, df1, &error_result, Policy())
88 && detail::check_df(
89 function, df2, &error_result, Policy())))
90 return error_result;
91
92 if((x < 0) || !(boost::math::isfinite)(x))
93 {
94 return policies::raise_domain_error<RealType>(
95 function, "Random variable parameter was %1%, but must be > 0 !", x, Policy());
96 }
97
98 if(x == 0)
99 {
100 // special cases:
101 if(df1 < 2)
102 return policies::raise_overflow_error<RealType>(
103 function, 0, Policy());
104 else if(df1 == 2)
105 return 1;
106 else
107 return 0;
108 }
109
110 //
111 // You reach this formula by direct differentiation of the
112 // cdf expressed in terms of the incomplete beta.
113 //
114 // There are two versions so we don't pass a value of z
115 // that is very close to 1 to ibeta_derivative: for some values
116 // of df1 and df2, all the change takes place in this area.
117 //
118 RealType v1x = df1 * x;
119 RealType result;
120 if(v1x > df2)
121 {
122 result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
123 result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
124 }
125 else
126 {
127 result = df2 + df1 * x;
128 result = (result * df1 - x * df1 * df1) / (result * result);
129 result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
130 }
131 return result;
132} // pdf
133
134template <class RealType, class Policy>
135inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
136{
137 static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
138 RealType df1 = dist.degrees_of_freedom1();
139 RealType df2 = dist.degrees_of_freedom2();
140 // Error check:
141 RealType error_result = 0;
142 if(false == detail::check_df(
143 function, df1, &error_result, Policy())
144 && detail::check_df(
145 function, df2, &error_result, Policy()))
146 return error_result;
147
148 if((x < 0) || !(boost::math::isfinite)(x))
149 {
150 return policies::raise_domain_error<RealType>(
151 function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
152 }
153
154 RealType v1x = df1 * x;
155 //
156 // There are two equivalent formulas used here, the aim is
157 // to prevent the final argument to the incomplete beta
158 // from being too close to 1: for some values of df1 and df2
159 // the rate of change can be arbitrarily large in this area,
160 // whilst the value we're passing will have lost information
161 // content as a result of being 0.999999something. Better
162 // to switch things around so we're passing 1-z instead.
163 //
164 return v1x > df2
165 ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
166 : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
167} // cdf
168
169template <class RealType, class Policy>
170inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p)
171{
172 static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
173 RealType df1 = dist.degrees_of_freedom1();
174 RealType df2 = dist.degrees_of_freedom2();
175 // Error check:
176 RealType error_result = 0;
177 if(false == (detail::check_df(
178 function, df1, &error_result, Policy())
179 && detail::check_df(
180 function, df2, &error_result, Policy())
181 && detail::check_probability(
182 function, p, &error_result, Policy())))
183 return error_result;
184
185 // With optimizations turned on, gcc wrongly warns about y being used
186 // uninitialized unless we initialize it to something:
187 RealType x, y(0);
188
189 x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy());
190
191 return df2 * x / (df1 * y);
192} // quantile
193
194template <class RealType, class Policy>
195inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
196{
197 static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
198 RealType df1 = c.dist.degrees_of_freedom1();
199 RealType df2 = c.dist.degrees_of_freedom2();
200 RealType x = c.param;
201 // Error check:
202 RealType error_result = 0;
203 if(false == detail::check_df(
204 function, df1, &error_result, Policy())
205 && detail::check_df(
206 function, df2, &error_result, Policy()))
207 return error_result;
208
209 if((x < 0) || !(boost::math::isfinite)(x))
210 {
211 return policies::raise_domain_error<RealType>(
212 function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
213 }
214
215 RealType v1x = df1 * x;
216 //
217 // There are two equivalent formulas used here, the aim is
218 // to prevent the final argument to the incomplete beta
219 // from being too close to 1: for some values of df1 and df2
220 // the rate of change can be arbitrarily large in this area,
221 // whilst the value we're passing will have lost information
222 // content as a result of being 0.999999something. Better
223 // to switch things around so we're passing 1-z instead.
224 //
225 return v1x > df2
226 ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
227 : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
228}
229
230template <class RealType, class Policy>
231inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
232{
233 static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
234 RealType df1 = c.dist.degrees_of_freedom1();
235 RealType df2 = c.dist.degrees_of_freedom2();
236 RealType p = c.param;
237 // Error check:
238 RealType error_result = 0;
239 if(false == (detail::check_df(
240 function, df1, &error_result, Policy())
241 && detail::check_df(
242 function, df2, &error_result, Policy())
243 && detail::check_probability(
244 function, p, &error_result, Policy())))
245 return error_result;
246
247 RealType x, y;
248
249 x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy());
250
251 return df2 * x / (df1 * y);
252}
253
254template <class RealType, class Policy>
255inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist)
256{ // Mean of F distribution = v.
257 static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)";
258 RealType df1 = dist.degrees_of_freedom1();
259 RealType df2 = dist.degrees_of_freedom2();
260 // Error check:
261 RealType error_result = 0;
262 if(false == detail::check_df(
263 function, df1, &error_result, Policy())
264 && detail::check_df(
265 function, df2, &error_result, Policy()))
266 return error_result;
267 if(df2 <= 2)
268 {
269 return policies::raise_domain_error<RealType>(
270 function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy());
271 }
272 return df2 / (df2 - 2);
273} // mean
274
275template <class RealType, class Policy>
276inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist)
277{ // Variance of F distribution.
278 static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)";
279 RealType df1 = dist.degrees_of_freedom1();
280 RealType df2 = dist.degrees_of_freedom2();
281 // Error check:
282 RealType error_result = 0;
283 if(false == detail::check_df(
284 function, df1, &error_result, Policy())
285 && detail::check_df(
286 function, df2, &error_result, Policy()))
287 return error_result;
288 if(df2 <= 4)
289 {
290 return policies::raise_domain_error<RealType>(
291 function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy());
292 }
293 return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
294} // variance
295
296template <class RealType, class Policy>
297inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist)
298{
299 static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)";
300 RealType df1 = dist.degrees_of_freedom1();
301 RealType df2 = dist.degrees_of_freedom2();
302 // Error check:
303 RealType error_result = 0;
304 if(false == detail::check_df(
305 function, df1, &error_result, Policy())
306 && detail::check_df(
307 function, df2, &error_result, Policy()))
308 return error_result;
309 if(df1 <= 2)
310 {
311 return policies::raise_domain_error<RealType>(
312 function, "First degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df1, Policy());
313 }
314 return df2 * (df1 - 2) / (df1 * (df2 + 2));
315}
316
317//template <class RealType, class Policy>
318//inline RealType median(const fisher_f_distribution<RealType, Policy>& dist)
319//{ // Median of Fisher F distribution is not defined.
320// return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
321// } // median
322
323// Now implemented via quantile(half) in derived accessors.
324
325template <class RealType, class Policy>
326inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist)
327{
328 static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)";
329 BOOST_MATH_STD_USING // ADL of std names
330 // See http://mathworld.wolfram.com/F-Distribution.html
331 RealType df1 = dist.degrees_of_freedom1();
332 RealType df2 = dist.degrees_of_freedom2();
333 // Error check:
334 RealType error_result = 0;
335 if(false == detail::check_df(
336 function, df1, &error_result, Policy())
337 && detail::check_df(
338 function, df2, &error_result, Policy()))
339 return error_result;
340 if(df2 <= 6)
341 {
342 return policies::raise_domain_error<RealType>(
343 function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy());
344 }
345 return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6);
346}
347
348template <class RealType, class Policy>
349RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist);
350
351template <class RealType, class Policy>
352inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist)
353{
354 return 3 + kurtosis_excess(dist);
355}
356
357template <class RealType, class Policy>
358inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist)
359{
360 static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)";
361 // See http://mathworld.wolfram.com/F-Distribution.html
362 RealType df1 = dist.degrees_of_freedom1();
363 RealType df2 = dist.degrees_of_freedom2();
364 // Error check:
365 RealType error_result = 0;
366 if(false == detail::check_df(
367 function, df1, &error_result, Policy())
368 && detail::check_df(
369 function, df2, &error_result, Policy()))
370 return error_result;
371 if(df2 <= 8)
372 {
373 return policies::raise_domain_error<RealType>(
374 function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kurtosis.", df2, Policy());
375 }
376 RealType df2_2 = df2 * df2;
377 RealType df1_2 = df1 * df1;
378 RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2;
379 n *= 12;
380 RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2);
381 return n / d;
382}
383
384} // namespace math
385} // namespace boost
386
387// This include must be at the end, *after* the accessors
388// for this distribution have been defined, in order to
389// keep compilers that support two-phase lookup happy.
390#include <boost/math/distributions/detail/derived_accessors.hpp>
391
392#endif // BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
393

source code of boost/libs/math/include/boost/math/distributions/fisher_f.hpp