1 // Copyright John Maddock 2006.
2 // Copyright Paul A. Bristow 2007, 2010.
3
4 // Use, modification and distribution are subject to the
5 // Boost Software License, Version 1.0.
6 // (See accompanying file LICENSE_1_0.txt
7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
8
9 // test_gamma_dist.cpp
10
11 // http://en.wikipedia.org/wiki/Gamma_distribution
12 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
13 // Also:
14 // Weisstein, Eric W. "Gamma Distribution."
15 // From MathWorld--A Wolfram Web Resource.
16 // http://mathworld.wolfram.com/GammaDistribution.html
17
18 #include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
19
20 #include <boost/math/concepts/real_concept.hpp> // for real_concept
21 #define BOOST_TEST_MAIN
22 #include <boost/test/unit_test.hpp> // Boost.Test
23 #include <boost/test/tools/floating_point_comparison.hpp>
24
25 #include <boost/math/distributions/gamma.hpp>
26 using boost::math::gamma_distribution;
27 #include <boost/math/tools/test.hpp>
28 #include "test_out_of_range.hpp"
29
30 #include <iostream>
31 #include <iomanip>
32 using std::cout;
33 using std::endl;
34 using std::setprecision;
35 #include <limits>
36 using std::numeric_limits;
37
38 template <class RealType>
NaivePDF(RealType shape,RealType scale,RealType x)39 RealType NaivePDF(RealType shape, RealType scale, RealType x)
40 {
41 // Deliberately naive PDF calculator again which
42 // we'll compare our pdf function. However some
43 // published values to compare against would be better....
44 using namespace std;
45 RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape;
46 return exp(result);
47 }
48
49 template <class RealType>
check_gamma(RealType shape,RealType scale,RealType x,RealType p,RealType q,RealType tol)50 void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
51 {
52 BOOST_CHECK_CLOSE(
53 ::boost::math::cdf(
54 gamma_distribution<RealType>(shape, scale), // distribution.
55 x), // random variable.
56 p, // probability.
57 tol); // %tolerance.
58 BOOST_CHECK_CLOSE(
59 ::boost::math::cdf(
60 complement(
61 gamma_distribution<RealType>(shape, scale), // distribution.
62 x)), // random variable.
63 q, // probability complement.
64 tol); // %tolerance.
65 if(p < 0.999)
66 {
67 BOOST_CHECK_CLOSE(
68 ::boost::math::quantile(
69 gamma_distribution<RealType>(shape, scale), // distribution.
70 p), // probability.
71 x, // random variable.
72 tol); // %tolerance.
73 }
74 if(q < 0.999)
75 {
76 BOOST_CHECK_CLOSE(
77 ::boost::math::quantile(
78 complement(
79 gamma_distribution<RealType>(shape, scale), // distribution.
80 q)), // probability complement.
81 x, // random variable.
82 tol); // %tolerance.
83 }
84 // PDF:
85 BOOST_CHECK_CLOSE(
86 boost::math::pdf(
87 gamma_distribution<RealType>(shape, scale), // distribution.
88 x), // random variable.
89 NaivePDF(shape, scale, x), // PDF
90 tol); // %tolerance.
91 }
92
93 template <class RealType>
test_spots(RealType)94 void test_spots(RealType)
95 {
96 // Basic sanity checks
97 //
98 // 15 decimal places expressed as a percentage.
99 // The first tests use values generated by MathCAD,
100 // and should be accurate to around double precision.
101 //
102 RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100;
103 cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
104
105 check_gamma(
106 static_cast<RealType>(0.5),
107 static_cast<RealType>(1),
108 static_cast<RealType>(0.5),
109 static_cast<RealType>(0.682689492137085),
110 static_cast<RealType>(1-0.682689492137085),
111 tolerance);
112 check_gamma(
113 static_cast<RealType>(2),
114 static_cast<RealType>(1),
115 static_cast<RealType>(0.5),
116 static_cast<RealType>(0.090204010431050),
117 static_cast<RealType>(1-0.090204010431050),
118 tolerance);
119 check_gamma(
120 static_cast<RealType>(40),
121 static_cast<RealType>(1),
122 static_cast<RealType>(10),
123 static_cast<RealType>(7.34163631456064E-13),
124 static_cast<RealType>(1-7.34163631456064E-13),
125 tolerance);
126
127 //
128 // Some more test data generated by the online
129 // calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
130 // This has the advantage of supporting the scale parameter as well
131 // as shape, but has only a few digits accuracy, and produces
132 // some deeply suspect values if the shape parameter is < 1
133 // (it doesn't agree with MathCAD or this implementation).
134 // To be fair the incomplete gamma is tricky to get right in this area...
135 //
136 tolerance = 1e-5f * 100; // 5 decimal places as a percentage
137 cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
138
139 check_gamma(
140 static_cast<RealType>(2),
141 static_cast<RealType>(1)/5,
142 static_cast<RealType>(0.1),
143 static_cast<RealType>(0.090204),
144 static_cast<RealType>(1-0.090204),
145 tolerance);
146 check_gamma(
147 static_cast<RealType>(2),
148 static_cast<RealType>(1)/5,
149 static_cast<RealType>(0.5),
150 static_cast<RealType>(1-0.287298),
151 static_cast<RealType>(0.287298),
152 tolerance);
153 check_gamma(
154 static_cast<RealType>(3),
155 static_cast<RealType>(2),
156 static_cast<RealType>(1),
157 static_cast<RealType>(0.014388),
158 static_cast<RealType>(1-0.014388),
159 tolerance * 10); // one less decimal place in the test value
160 check_gamma(
161 static_cast<RealType>(3),
162 static_cast<RealType>(2),
163 static_cast<RealType>(5),
164 static_cast<RealType>(0.456187),
165 static_cast<RealType>(1-0.456187),
166 tolerance);
167
168
169 RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
170 gamma_distribution<RealType> dist(8, 3);
171 RealType x = static_cast<RealType>(0.125);
172 using namespace std; // ADL of std names.
173 // mean:
174 BOOST_CHECK_CLOSE(
175 mean(dist)
176 , static_cast<RealType>(8*3), tol2);
177 // variance:
178 BOOST_CHECK_CLOSE(
179 variance(dist)
180 , static_cast<RealType>(8*3*3), tol2);
181 // std deviation:
182 BOOST_CHECK_CLOSE(
183 standard_deviation(dist)
184 , sqrt(static_cast<RealType>(8*3*3)), tol2);
185 // hazard:
186 BOOST_CHECK_CLOSE(
187 hazard(dist, x)
188 , pdf(dist, x) / cdf(complement(dist, x)), tol2);
189 // cumulative hazard:
190 BOOST_CHECK_CLOSE(
191 chf(dist, x)
192 , -log(cdf(complement(dist, x))), tol2);
193 // coefficient_of_variation:
194 BOOST_CHECK_CLOSE(
195 coefficient_of_variation(dist)
196 , standard_deviation(dist) / mean(dist), tol2);
197 // mode:
198 BOOST_CHECK_CLOSE(
199 mode(dist)
200 , static_cast<RealType>(7 * 3), tol2);
201 // skewness:
202 BOOST_CHECK_CLOSE(
203 skewness(dist)
204 , 2 / sqrt(static_cast<RealType>(8)), tol2);
205 // kurtosis:
206 BOOST_CHECK_CLOSE(
207 kurtosis(dist)
208 , 3 + 6 / static_cast<RealType>(8), tol2);
209 // kurtosis excess:
210 BOOST_CHECK_CLOSE(
211 kurtosis_excess(dist)
212 , 6 / static_cast<RealType>(8), tol2);
213
214 BOOST_CHECK_CLOSE(
215 median(dist), static_cast<RealType>(23.007748327502412), // double precision test value
216 (std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as percent
217
218 using std::log;
219 RealType expected_entropy = RealType(8) + log(RealType(3)) + boost::math::lgamma(RealType(8)) - 7*boost::math::digamma(RealType(8));
220 BOOST_CHECK_CLOSE(
221 entropy(dist), expected_entropy, tol2);
222
223 // Rely on default definition in derived accessors.
224
225 // error tests
226 check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1);
227 BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error);
228 BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error);
229 BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error);
230 BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error);
231
232 } // template <class RealType>void test_spots(RealType)
233
BOOST_AUTO_TEST_CASE(test_main)234 BOOST_AUTO_TEST_CASE( test_main )
235 {
236 // Basic sanity-check spot values.
237 // (Parameter value, arbitrarily zero, only communicates the floating point type).
238 test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
239 test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
240 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
241 test_spots(0.0L); // Test long double.
242 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
243 test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
244 #endif
245 #else
246 std::cout << "<note>The long double tests have been disabled on this platform "
247 "either because the long double overloads of the usual math functions are "
248 "not available at all, or because they are too inaccurate for these tests "
249 "to pass.</note>" << std::endl;
250 #endif
251
252
253 } // BOOST_AUTO_TEST_CASE( test_main )
254
255
256 /*
257
258 Output:
259
260 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe"
261 Running 1 test case...
262 Tolerance for type float is 0.000238419 %
263 Tolerance for type float is 0.001 %
264 Tolerance for type double is 5e-012 %
265 Tolerance for type double is 0.001 %
266 Tolerance for type long double is 5e-012 %
267 Tolerance for type long double is 0.001 %
268 Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
269 Tolerance for type class boost::math::concepts::real_concept is 0.001 %
270 *** No errors detected
271
272 */
273
274
275