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- // Copyright Paul A. Bristow 2007, 2009.
- // Copyright John Maddock 2006.
- // 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/test.hpp> // for real_concept
- #include <boost/math/concepts/real_concept.hpp> // for real_concept
- #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 <boost/math/tools/test.hpp>
- #include "test_out_of_range.hpp"
- #include <iostream>
- using std::cout;
- using std::endl;
- using std::setprecision;
- #include <limits>
- using std::numeric_limits;
- template <class RealType>
- void check_pareto(RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
- {
- 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::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);
- // kertosis:
- BOOST_CHECK_CLOSE_FRACTION(
- kurtosis(pareto15), static_cast<RealType>(73.8L), tol5eps);
- // kertosis 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;
- // 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(__BORLANDC__, BOOST_TESTED_AT(0x0582))
- 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
- */
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