// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007
// 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_lognormal.cpp
#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/lognormal.hpp>
using boost::math::lognormal_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;
#include <cassert>
template <class RealType>
void check_lognormal(RealType loc, RealType scale, RealType x, RealType p, RealType q, RealType tol)
{
BOOST_CHECK_CLOSE(
::boost::math::cdf(
lognormal_distribution<RealType>(loc, scale), // distribution.
x), // random variable.
p, // probability.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(
lognormal_distribution<RealType>(loc, scale), // distribution.
x)), // random variable.
q, // probability complement.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::quantile(
lognormal_distribution<RealType>(loc, scale), // distribution.
p), // probability.
x, // random variable.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(
lognormal_distribution<RealType>(loc, scale), // distribution.
q)), // probability complement.
x, // random variable.
tol); // %tolerance.
}
template <class RealType>
void test_spots(RealType)
{
// Basic sanity checks.
RealType tolerance = 5e-3 * 100;
// Some tests only pass at 1e-4 because values generated by
// http://faculty.vassar.edu/lowry/VassarStats.html
// give only 5 or 6 *fixed* places, so small values have fewer digits.
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
using std::exp;
//
// These test values were generated for the normal distribution
// using the online calculator at http://faculty.vassar.edu/lowry/VassarStats.html
// and then exponentiating the random variate x.
//
check_lognormal(
static_cast<RealType>(0), // location
static_cast<RealType>(5), // scale
static_cast<RealType>(1), // x
static_cast<RealType>(0.5), // p
static_cast<RealType>(0.5), // q
tolerance);
check_lognormal(
static_cast<RealType>(2), // location
static_cast<RealType>(2), // scale
static_cast<RealType>(exp(1.8)), // x
static_cast<RealType>(0.46017), // p
static_cast<RealType>(1-0.46017), // q
tolerance);
check_lognormal(
static_cast<RealType>(2), // location
static_cast<RealType>(2), // scale
static_cast<RealType>(exp(2.2)), // x
static_cast<RealType>(1-0.46017), // p
static_cast<RealType>(0.46017), // q
tolerance);
check_lognormal(
static_cast<RealType>(2), // location
static_cast<RealType>(2), // scale
static_cast<RealType>(exp(-1.4)), // x
static_cast<RealType>(0.04457), // p
static_cast<RealType>(1-0.04457), // q
tolerance);
check_lognormal(
static_cast<RealType>(2), // location
static_cast<RealType>(2), // scale
static_cast<RealType>(exp(5.4)), // x
static_cast<RealType>(1-0.04457), // p
static_cast<RealType>(0.04457), // q
tolerance);
check_lognormal(
static_cast<RealType>(-3), // location
static_cast<RealType>(5), // scale
static_cast<RealType>(exp(-5.0)), // x
static_cast<RealType>(0.34458), // p
static_cast<RealType>(1-0.34458), // q
tolerance);
check_lognormal(
static_cast<RealType>(-3), // location
static_cast<RealType>(5), // scale
static_cast<RealType>(exp(-1.0)), // x
static_cast<RealType>(1-0.34458), // p
static_cast<RealType>(0.34458), // q
tolerance);
check_lognormal(
static_cast<RealType>(-3), // location
static_cast<RealType>(5), // scale
static_cast<RealType>(exp(-9.0)), // x
static_cast<RealType>(0.11507), // p
static_cast<RealType>(1-0.11507), // q
tolerance);
check_lognormal(
static_cast<RealType>(-3), // location
static_cast<RealType>(5), // scale
static_cast<RealType>(exp(3.0)), // x
static_cast<RealType>(1-0.11507), // p
static_cast<RealType>(0.11507), // q
tolerance);
//
// Tests for PDF
//
tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
BOOST_CHECK_CLOSE(
pdf(lognormal_distribution<RealType>(), static_cast<RealType>(1)),
static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
tolerance);
BOOST_CHECK_CLOSE(
pdf(lognormal_distribution<RealType>(3), exp(static_cast<RealType>(3))),
static_cast<RealType>(0.3989422804014326779399460599343818684759L) / exp(static_cast<RealType>(3)),
tolerance);
BOOST_CHECK_CLOSE(
pdf(lognormal_distribution<RealType>(3, 5), exp(static_cast<RealType>(3))),
static_cast<RealType>(0.3989422804014326779399460599343818684759L / (5 * exp(static_cast<RealType>(3)))),
tolerance);
//
// Spot checks for location = -5, scale = 6,
// use relation to normal to test:
//
for(RealType x = -15; x < 5; x += 0.125)
{
BOOST_CHECK_CLOSE(
pdf(lognormal_distribution<RealType>(-5, 6), exp(x)),
pdf(boost::math::normal_distribution<RealType>(-5, 6), x) / exp(x),
tolerance);
}
//
// These test values were obtained by punching numbers into
// a calculator, using the formulas at http://mathworld.wolfram.com/LogNormalDistribution.html
//
tolerance = (std::max)(
boost::math::tools::epsilon<RealType>(),
static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5 * 100; // 5 eps as a percentage
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
lognormal_distribution<RealType> dist(8, 3);
RealType x = static_cast<RealType>(0.125);
BOOST_MATH_STD_USING // ADL of std math lib names.
// mean:
BOOST_CHECK_CLOSE(
mean(dist)
, static_cast<RealType>(268337.28652087445695647967378715L), tolerance);
// variance:
BOOST_CHECK_CLOSE(
variance(dist)
, static_cast<RealType>(583389737628117.49553037857325892L), tolerance);
// std deviation:
BOOST_CHECK_CLOSE(
standard_deviation(dist)
, static_cast<RealType>(24153462.228594009489719473727471L), tolerance);
// hazard:
BOOST_CHECK_CLOSE(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tolerance);
// cumulative hazard:
BOOST_CHECK_CLOSE(
chf(dist, x)
, -log(cdf(complement(dist, x))), tolerance);
// coefficient_of_variation:
BOOST_CHECK_CLOSE(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tolerance);
// mode:
BOOST_CHECK_CLOSE(
mode(dist)
, static_cast<RealType>(0.36787944117144232159552377016146L), tolerance);
BOOST_CHECK_CLOSE(
median(dist)
, static_cast<RealType>(exp(dist.location())), tolerance);
BOOST_CHECK_CLOSE(
median(dist),
quantile(dist, static_cast<RealType>(0.5)), tolerance);
// skewness:
BOOST_CHECK_CLOSE(
skewness(dist)
, static_cast<RealType>(729551.38304660255658441529235697L), tolerance);
// kertosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, static_cast<RealType>(4312295840576303.2363383232038251L), tolerance);
// kertosis excess:
BOOST_CHECK_CLOSE(
kurtosis_excess(dist)
, static_cast<RealType>(4312295840576300.2363383232038251L), tolerance);
BOOST_CHECK_CLOSE(
range(dist).first
, static_cast<RealType>(0), tolerance);
//
// Special cases:
//
BOOST_CHECK(pdf(dist, 0) == 0);
BOOST_CHECK(cdf(dist, 0) == 0);
BOOST_CHECK(cdf(complement(dist, 0)) == 1);
BOOST_CHECK(quantile(dist, 0) == 0);
BOOST_CHECK(quantile(complement(dist, 1)) == 0);
//
// Error checks:
//
BOOST_MATH_CHECK_THROW(lognormal_distribution<RealType>(0, 0), std::domain_error);
BOOST_MATH_CHECK_THROW(lognormal_distribution<RealType>(2, -1), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(dist, 1), std::overflow_error);
BOOST_MATH_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error);
check_out_of_range<lognormal_distribution<RealType> >(1, 2);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
// Check that can generate lognormal distribution using the two convenience methods:
boost::math::lognormal myf1(1., 2); // Using typedef
lognormal_distribution<> myf2(1., 2); // Using default RealType double.
// Test range and support using double only,
// because it supports numeric_limits max for a pseudo-infinity.
BOOST_CHECK_EQUAL(range(myf2).first, 0); // range 0 to +infinity
BOOST_CHECK_EQUAL(range(myf2).second, (std::numeric_limits<double>::max)());
BOOST_CHECK_EQUAL(support(myf2).first, 0); // support 0 to + infinity.
BOOST_CHECK_EQUAL(support(myf2).second, (std::numeric_limits<double>::max)());
// Basic sanity-check spot values.
// (Parameter value, arbitrarily zero, only communicates the floating point type).
test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 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 )
/*
Running 1 test case...
Tolerance for type float is 0.5 %
Tolerance for type float is 5.96046e-005 %
Tolerance for type float is 5.96046e-005 %
Tolerance for type double is 0.5 %
Tolerance for type double is 1.11022e-013 %
Tolerance for type double is 1.11022e-013 %
Tolerance for type long double is 0.5 %
Tolerance for type long double is 1.11022e-013 %
Tolerance for type long double is 1.11022e-013 %
Tolerance for type class boost::math::concepts::real_concept is 0.5 %
Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 %
Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 %
*** No errors detected
*/