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
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
|
// Copyright Paul A. Bristow 2007, 2009.
// Copyright John Maddock 2006.
// Copyright Matt Borland 2023.
// Use, modification and distribution are subject to 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)
// test_pareto.cpp
// http://en.wikipedia.org/wiki/pareto_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
// Also:
// Weisstein, Eric W. "pareto Distribution."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/paretoDistribution.html
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
# pragma warning (disable : 4996) // POSIX name for this item is deprecated
# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'arg' was previously defined as a type
# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored
# pragma warning(disable: 4100) // unreferenced formal parameter.
#endif
#include <boost/math/tools/config.hpp>
#include "../include_private/boost/math/tools/test.hpp"
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#endif
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // Boost.Test
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/distributions/pareto.hpp>
using boost::math::pareto_distribution;
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
using std::setprecision;
#include <limits>
using std::numeric_limits;
#include <type_traits>
template <class RealType>
void check_pareto(RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
{
RealType logtol = tol * 10;
#ifndef BOOST_MATH_HAS_GPU_SUPPORT
BOOST_IF_CONSTEXPR (std::is_same<RealType, long double>::value ||
std::is_same<RealType, boost::math::concepts::real_concept>::value)
{
logtol *= 100;
}
#endif
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::cdf(
pareto_distribution<RealType>(scale, shape), // distribution.
x), // random variable.
p, // probability.
tol); // tolerance eps.
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::cdf(
complement(
pareto_distribution<RealType>(scale, shape), // distribution.
x)), // random variable.
q, // probability complement.
tol); // tolerance eps.
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::logcdf(
pareto_distribution<RealType>(scale, shape), // distribution.
x), // random variable.
log(p), // probability.
logtol); // tolerance eps.
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::logcdf(
complement(
pareto_distribution<RealType>(scale, shape), // distribution.
x)), // random variable.
log(q), // probability complement.
logtol); // tolerance eps.
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::quantile(
pareto_distribution<RealType>(scale, shape), // distribution.
p), // probability.
x, // random variable.
tol); // tolerance eps.
BOOST_CHECK_CLOSE_FRACTION(
::boost::math::quantile(
complement(
pareto_distribution<RealType>(scale, shape), // distribution.
q)), // probability complement.
x, // random variable.
tol); // tolerance eps.
} // check_pareto
template <class RealType>
void test_spots(RealType)
{
// Basic sanity checks.
//
// Tolerance are based on units of epsilon, but capped at
// double precision, since that's the limit of our test data:
//
RealType tol = (std::max)((RealType)boost::math::tools::epsilon<double>(), boost::math::tools::epsilon<RealType>());
RealType tol5eps = tol * 5;
RealType tol10eps = tol * 10;
RealType tol100eps = tol * 100;
RealType tol1000eps = tol * 1000;
check_pareto(
static_cast<RealType>(1.1L), //
static_cast<RealType>(5.5L),
static_cast<RealType>(2.2L),
static_cast<RealType>(0.97790291308792L),
static_cast<RealType>(0.0220970869120796L),
tol10eps * 4);
check_pareto(
static_cast<RealType>(0.5L),
static_cast<RealType>(10.1L),
static_cast<RealType>(1.5L),
static_cast<RealType>(0.99998482686481L),
static_cast<RealType>(1.51731351900608e-005L),
tol100eps * 1000); // Much less accurate as p close to unity.
check_pareto(
static_cast<RealType>(0.1L),
static_cast<RealType>(2.3L),
static_cast<RealType>(1.5L),
static_cast<RealType>(0.99802762220697L),
static_cast<RealType>(0.00197237779302972L),
tol1000eps);
// Example from 23.3 page 259
check_pareto(
static_cast<RealType>(2.30444301457005L),
static_cast<RealType>(4),
static_cast<RealType>(2.4L),
static_cast<RealType>(0.15L),
static_cast<RealType>(0.85L),
tol100eps);
check_pareto(
static_cast<RealType>(2),
static_cast<RealType>(3),
static_cast<RealType>(3.4L),
static_cast<RealType>(0.796458375737838L),
static_cast<RealType>(0.203541624262162L),
tol10eps);
check_pareto( // Probability near 0.5
static_cast<RealType>(2),
static_cast<RealType>(2),
static_cast<RealType>(3),
static_cast<RealType>(0.5555555555555555555555555555555555555556L),
static_cast<RealType>(0.4444444444444444444444444444444444444444L),
tol5eps); // accurate.
// Tests for:
// pdf for shapes 1, 2 & 3 (exact)
BOOST_CHECK_CLOSE_FRACTION(
pdf(pareto_distribution<RealType>(1, 1), 1),
static_cast<RealType>(1), //
tol5eps);
BOOST_CHECK_CLOSE_FRACTION( pdf(pareto_distribution<RealType>(1, 2), 1),
static_cast<RealType>(2), //
tol5eps);
BOOST_CHECK_CLOSE_FRACTION( pdf(pareto_distribution<RealType>(1, 3), 1),
static_cast<RealType>(3), //
tol5eps);
// cdf
BOOST_CHECK_EQUAL( // x = scale
cdf(pareto_distribution<RealType>(1, 1), 1),
static_cast<RealType>(0) );
// Compare with values from StatCalc K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3
BOOST_CHECK_CLOSE_FRACTION( // small x
cdf(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4)),
static_cast<RealType>(0.929570372227626L), tol5eps);
BOOST_CHECK_CLOSE_FRACTION( // small x
cdf(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4)),
static_cast<RealType>(1 - 0.0704296277723743L), tol5eps);
BOOST_CHECK_CLOSE_FRACTION( // small x
cdf(complement(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4))),
static_cast<RealType>(0.0704296277723743L), tol5eps);
// quantile
BOOST_CHECK_EQUAL( // x = scale
quantile(pareto_distribution<RealType>(1, 1), 0),
static_cast<RealType>(1) );
BOOST_CHECK_EQUAL( // x = scale
quantile(complement(pareto_distribution<RealType>(1, 1), 1)),
static_cast<RealType>(1) );
BOOST_CHECK_CLOSE_FRACTION( // small x
cdf(complement(pareto_distribution<RealType>(2, 5), static_cast<RealType>(3.4))),
static_cast<RealType>(0.0704296277723743L), tol5eps);
using namespace std; // ADL of std names.
pareto_distribution<RealType> pareto15(1, 5);
// Note: shape must be big enough (5) that all moments up to kurtosis are defined
// to allow all functions to be tested.
// mean:
BOOST_CHECK_CLOSE_FRACTION(
mean(pareto15), static_cast<RealType>(1.25), tol5eps); // 1.25 == 5/4
BOOST_CHECK_EQUAL(
mean(pareto15), static_cast<RealType>(1.25)); // 1.25 == 5/4 (expect exact so check equal)
pareto_distribution<RealType> p12(1, 2); //
BOOST_CHECK_EQUAL(
mean(p12), static_cast<RealType>(2)); // Exactly two.
// variance:
BOOST_CHECK_CLOSE_FRACTION(
variance(pareto15), static_cast<RealType>(0.10416666666666667L), tol5eps);
// std deviation:
BOOST_CHECK_CLOSE_FRACTION(
standard_deviation(pareto15), static_cast<RealType>(0.32274861218395140L), tol5eps);
// hazard: No independent test values found yet.
//BOOST_CHECK_CLOSE_FRACTION(
// hazard(pareto15, x), pdf(pareto15, x) / cdf(complement(pareto15, x)), tol5eps);
//// cumulative hazard:
//BOOST_CHECK_CLOSE_FRACTION(
// chf(pareto15, x), -log(cdf(complement(pareto15, x))), tol5eps);
//// coefficient_of_variation:
BOOST_CHECK_CLOSE_FRACTION(
coefficient_of_variation(pareto15), static_cast<RealType>(0.25819888974716110L), tol5eps);
// mode:
BOOST_CHECK_CLOSE_FRACTION(
mode(pareto15), static_cast<RealType>(1), tol5eps);
BOOST_CHECK_CLOSE_FRACTION(
median(pareto15), static_cast<RealType>(1.1486983549970351L), tol5eps);
// skewness:
BOOST_CHECK_CLOSE_FRACTION(
skewness(pareto15), static_cast<RealType>(4.6475800154489004L), tol5eps);
// kurtosis:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis(pareto15), static_cast<RealType>(73.8L), tol5eps);
// kurtosis excess:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(pareto15), static_cast<RealType>(70.8L), tol5eps);
// Check difference between kurtosis and excess:
BOOST_CHECK_CLOSE_FRACTION(
kurtosis_excess(pareto15), kurtosis(pareto15) - static_cast<RealType>(3L), tol5eps);
// Check kurtosis excess = kurtosis - 3;
RealType expected_entropy = 1 + RealType(1)/RealType(5) + log(RealType(1)/RealType(5));
BOOST_CHECK_CLOSE_FRACTION(
entropy(pareto15), expected_entropy, tol5eps);
// Error condition checks:
check_out_of_range<pareto_distribution<RealType> >(1, 1);
BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(0, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, 0), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(-1, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, -1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(pareto_distribution<RealType>(1, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(cdf(pareto_distribution<RealType>(1, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(pareto_distribution<RealType>(1, 1), -1), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(pareto_distribution<RealType>(1, 1), 2), std::domain_error);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
// Check that can generate pareto distribution using the two convenience methods:
boost::math::pareto myp1(1., 1); // Using typedef
pareto_distribution<> myp2(1., 1); // Using default RealType double.
boost::math::pareto pareto11; // Use default values (scale = 1, shape = 1).
// Note NOT pareto11() as the compiler will interpret as a function!
// Basic sanity-check spot values.
BOOST_CHECK_EQUAL(pareto11.scale(), 1); // Check defaults again.
BOOST_CHECK_EQUAL(pareto11.shape(), 1);
BOOST_CHECK_EQUAL(myp1.scale(), 1);
BOOST_CHECK_EQUAL(myp1.shape(), 1);
BOOST_CHECK_EQUAL(myp2.scale(), 1);
BOOST_CHECK_EQUAL(myp2.shape(), 1);
// Test range and support using double only,
// because it supports numeric_limits max for pseudo-infinity.
BOOST_CHECK_EQUAL(range(myp2).first, 0); // range 0 to +infinity
BOOST_CHECK_EQUAL(range(myp2).second, (numeric_limits<double>::max)());
BOOST_CHECK_EQUAL(support(myp2).first, myp2.scale()); // support scale to + infinity.
BOOST_CHECK_EQUAL(support(myp2).second, (numeric_limits<double>::max)());
// Check some bad parameters to the distribution.
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(boost::math::pareto mypm1(-1, 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto myp0(0, 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto myp1m1(1, -1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto myp10(1, 0), std::domain_error); // Using typedef
#else
BOOST_MATH_CHECK_THROW(boost::math::pareto(-1, 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto(0, 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto(1, -1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto(1, 0), std::domain_error); // Using typedef
#endif
// Check some moments that should fail because shape not big enough.
BOOST_MATH_CHECK_THROW(variance(myp2), std::domain_error);
BOOST_MATH_CHECK_THROW(standard_deviation(myp2), std::domain_error);
BOOST_MATH_CHECK_THROW(skewness(myp2), std::domain_error);
BOOST_MATH_CHECK_THROW(kurtosis(myp2), std::domain_error);
BOOST_MATH_CHECK_THROW(kurtosis_excess(myp2), std::domain_error);
// Test on extreme values of distribution parameters,
// using just double because it has numeric_limit infinity etc.
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(boost::math::pareto mypinf1(+std::numeric_limits<double>::infinity(), 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto myp1inf(1, +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto mypinf1(+std::numeric_limits<double>::infinity(), +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
#else
BOOST_MATH_CHECK_THROW(boost::math::pareto(+std::numeric_limits<double>::infinity(), 1), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto(1, +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
BOOST_MATH_CHECK_THROW(boost::math::pareto(+std::numeric_limits<double>::infinity(), +std::numeric_limits<double>::infinity()), std::domain_error); // Using typedef
#endif
// Test on extreme values of random variate x, using just double because it has numeric_limit infinity etc..
// No longer allow x to be + or - infinity, then these tests should throw.
BOOST_MATH_CHECK_THROW(pdf(pareto11, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
BOOST_MATH_CHECK_THROW(pdf(pareto11, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
BOOST_MATH_CHECK_THROW(cdf(pareto11, +std::numeric_limits<double>::infinity()), std::domain_error); // x = + infinity
BOOST_MATH_CHECK_THROW(cdf(pareto11, -std::numeric_limits<double>::infinity()), std::domain_error); // x = - infinity
BOOST_CHECK_EQUAL(pdf(pareto11, 0.5), 0); // x < scale but > 0
BOOST_CHECK_EQUAL(pdf(pareto11, (std::numeric_limits<double>::min)()), 0); // x almost zero but > 0
BOOST_CHECK_EQUAL(pdf(pareto11, 1), 1); // x == scale, result == shape == 1
BOOST_CHECK_EQUAL(pdf(pareto11, +(std::numeric_limits<double>::max)()), 0); // x = +max, pdf has fallen to zero.
BOOST_MATH_CHECK_THROW(pdf(pareto11, 0), std::domain_error); // x == 0
BOOST_MATH_CHECK_THROW(pdf(pareto11, -1), std::domain_error); // x = -1
BOOST_MATH_CHECK_THROW(pdf(pareto11, -(std::numeric_limits<double>::max)()), std::domain_error); // x = - max
BOOST_MATH_CHECK_THROW(pdf(pareto11, -(std::numeric_limits<double>::min)()), std::domain_error); // x = - min
BOOST_CHECK_EQUAL(cdf(pareto11, 1), 0); // x == scale, cdf = zero.
BOOST_CHECK_EQUAL(cdf(pareto11, +(std::numeric_limits<double>::max)()), 1); // x = + max, cdf = unity.
BOOST_MATH_CHECK_THROW(cdf(pareto11, 0), std::domain_error); // x == 0
BOOST_MATH_CHECK_THROW(cdf(pareto11, -(std::numeric_limits<double>::min)()), std::domain_error); // x = - min,
BOOST_MATH_CHECK_THROW(cdf(pareto11, -(std::numeric_limits<double>::max)()), std::domain_error); // x = - max,
// (Parameter value, arbitrarily zero, only communicates the floating point type).
test_spots(0.0F); // Test float. OK at decdigits = 0 tol5eps = 0.0001 %
test_spots(0.0); // Test double. OK at decdigits 7, tol5eps = 1e07 %
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L); // Test long double.
#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
} // BOOST_AUTO_TEST_CASE( test_main )
/*
Output:
Compiling...
test_pareto.cpp
Linking...
Embedding manifest...
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_pareto.exe"
Running 1 test case...
*** No errors detected
*/
|
