--- /dev/null
+// 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/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
+
+
+
+*/
+
+
projects / ceph.git / blobdiff