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// Copyright Paul A. Bristow 2007.
// Copyright John Maddock 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_normal.cpp
// http://en.wikipedia.org/wiki/Normal_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
// Also:
// Weisstein, Eric W. "Normal Distribution."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/NormalDistribution.html
#ifdef _MSC_VER
#pragma warning (disable: 4127) // conditional expression is constant
// caused by using if(std::numeric_limits<RealType>::has_infinity)
// and if (std::numeric_limits<RealType>::has_quiet_NaN)
#endif
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/test/included/test_exec_monitor.hpp> // Boost.Test
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/distributions/normal.hpp>
using boost::math::normal_distribution;
#include <boost/math/tools/test.hpp>
#include <iostream>
using std::cout;
using std::endl;
using std::setprecision;
#include <limits>
using std::numeric_limits;
template <class RealType>
RealType NaivePDF(RealType mean, RealType sd, RealType x)
{
// Deliberately naive PDF calculator again which
// we'll compare our pdf function. However some
// published values to compare against would be better....
using namespace std;
return exp(-(x-mean)*(x-mean)/(2*sd*sd))/(sd * sqrt(2*boost::math::constants::pi<RealType>()));
}
template <class RealType>
void check_normal(RealType mean, RealType sd, RealType x, RealType p, RealType q, RealType tol)
{
BOOST_CHECK_CLOSE(
::boost::math::cdf(
normal_distribution<RealType>(mean, sd), // distribution.
x), // random variable.
p, // probability.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(
normal_distribution<RealType>(mean, sd), // distribution.
x)), // random variable.
q, // probability complement.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::quantile(
normal_distribution<RealType>(mean, sd), // distribution.
p), // probability.
x, // random variable.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(
normal_distribution<RealType>(mean, sd), // distribution.
q)), // probability complement.
x, // random variable.
tol); // %tolerance.
}
template <class RealType>
void test_spots(RealType)
{
// Basic sanity checks
RealType tolerance = 1e-2f; // 1e-4 (as %)
// 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.
// Check some bad parameters to the distribution,
BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
// Tests on extreme values of random variate x, if has numeric_limit infinity etc.
normal_distribution<RealType> N01;
if(std::numeric_limits<RealType>::has_infinity)
{
BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
BOOST_CHECK_THROW(boost::math::normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
}
if (std::numeric_limits<RealType>::has_quiet_NaN)
{
// No longer allow x to be NaN, then these tests should throw.
BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
BOOST_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
}
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
check_normal(
static_cast<RealType>(5),
static_cast<RealType>(2),
static_cast<RealType>(4.8),
static_cast<RealType>(0.46017),
static_cast<RealType>(1 - 0.46017),
tolerance);
check_normal(
static_cast<RealType>(5),
static_cast<RealType>(2),
static_cast<RealType>(5.2),
static_cast<RealType>(1 - 0.46017),
static_cast<RealType>(0.46017),
tolerance);
check_normal(
static_cast<RealType>(5),
static_cast<RealType>(2),
static_cast<RealType>(2.2),
static_cast<RealType>(0.08076),
static_cast<RealType>(1 - 0.08076),
tolerance);
check_normal(
static_cast<RealType>(5),
static_cast<RealType>(2),
static_cast<RealType>(7.8),
static_cast<RealType>(1 - 0.08076),
static_cast<RealType>(0.08076),
tolerance);
check_normal(
static_cast<RealType>(-3),
static_cast<RealType>(5),
static_cast<RealType>(-4.5),
static_cast<RealType>(0.38209),
static_cast<RealType>(1 - 0.38209),
tolerance);
check_normal(
static_cast<RealType>(-3),
static_cast<RealType>(5),
static_cast<RealType>(-1.5),
static_cast<RealType>(1 - 0.38209),
static_cast<RealType>(0.38209),
tolerance);
check_normal(
static_cast<RealType>(-3),
static_cast<RealType>(5),
static_cast<RealType>(-8.5),
static_cast<RealType>(0.13567),
static_cast<RealType>(1 - 0.13567),
tolerance);
check_normal(
static_cast<RealType>(-3),
static_cast<RealType>(5),
static_cast<RealType>(2.5),
static_cast<RealType>(1 - 0.13567),
static_cast<RealType>(0.13567),
tolerance);
//
// Tests for PDF: we know that the peak value is at 1/sqrt(2*pi)
//
tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
BOOST_CHECK_CLOSE(
pdf(normal_distribution<RealType>(), static_cast<RealType>(0)),
static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
tolerance);
BOOST_CHECK_CLOSE(
pdf(normal_distribution<RealType>(3), static_cast<RealType>(3)),
static_cast<RealType>(0.3989422804014326779399460599343818684759L),
tolerance);
BOOST_CHECK_CLOSE(
pdf(normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
tolerance);
//
// Spot checks for mean = -5, sd = 6:
//
for(RealType x = -15; x < 5; x += 0.125)
{
BOOST_CHECK_CLOSE(
pdf(normal_distribution<RealType>(-5, 6), x),
NaivePDF(RealType(-5), RealType(6), x),
tolerance);
}
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5;
normal_distribution<RealType> dist(8, 3);
RealType x = static_cast<RealType>(0.125);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE(
mean(dist)
, static_cast<RealType>(8), tol2);
// variance:
BOOST_CHECK_CLOSE(
variance(dist)
, static_cast<RealType>(9), tol2);
// std deviation:
BOOST_CHECK_CLOSE(
standard_deviation(dist)
, static_cast<RealType>(3), tol2);
// hazard:
BOOST_CHECK_CLOSE(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
// cumulative hazard:
BOOST_CHECK_CLOSE(
chf(dist, x)
, -log(cdf(complement(dist, x))), tol2);
// coefficient_of_variation:
BOOST_CHECK_CLOSE(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tol2);
// mode:
BOOST_CHECK_CLOSE(
mode(dist)
, static_cast<RealType>(8), tol2);
BOOST_CHECK_CLOSE(
median(dist)
, static_cast<RealType>(8), tol2);
// skewness:
BOOST_CHECK_CLOSE(
skewness(dist)
, static_cast<RealType>(0), tol2);
// kertosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, static_cast<RealType>(3), tol2);
// kertosis excess:
BOOST_CHECK_CLOSE(
kurtosis_excess(dist)
, static_cast<RealType>(0), tol2);
normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
BOOST_CHECK_CLOSE(
mean(norm01),
static_cast<RealType>(0), 0); // Mean == zero
normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
BOOST_CHECK_CLOSE(
mean(defsd_norm01),
static_cast<RealType>(0), 0); // Mean == zero
normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
BOOST_CHECK_CLOSE(
mean(def_norm01),
static_cast<RealType>(0), 0); // Mean == zero
BOOST_CHECK_CLOSE(
standard_deviation(def_norm01),
static_cast<RealType>(1), 0); // Mean == zero
} // template <class RealType>void test_spots(RealType)
int test_main(int, char* [])
{
// Check that can generate normal distribution using the two convenience methods:
boost::math::normal myf1(1., 2); // Using typedef
normal_distribution<> myf2(1., 2); // Using default RealType double.
boost::math::normal myn01; // Use default values.
// Note NOT myn01() as the compiler will interpret as a function!
// Check the synonyms, provided to allow generic use of find_location and find_scale.
BOOST_CHECK_EQUAL(myn01.mean(), myn01.location());
BOOST_CHECK_EQUAL(myn01.standard_deviation(), myn01.scale());
// 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::cout;
#endif
return 0;
} // int test_main(int, char* [])
/*
Output:
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_normal.exe"
Running 1 test case...
Tolerance for type float is 0.01 %
Tolerance for type double is 0.01 %
Tolerance for type long double is 0.01 %
Tolerance for type class boost::math::concepts::real_concept is 0.01 %
*** No errors detected
*/
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