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math/test/test_cauchy.cpp
John Maddock 1555938251 Added scale and location parameters to Cauchy. 
[SVN r3253]
2006-10-14 18:03:03 +00:00

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// 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_students_t.cpp
#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
# pragma warning(disable: 4100) // unreferenced formal parameter.
# pragma warning(disable: 4512) // assignment operator could not be generated.
# pragma warning(disable: 4510) // default constructor could not be generated.
# pragma warning(disable: 4610) // can never be instantiated - user defined constructor required.
//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
#endif
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/cauchy.hpp>
using boost::math::cauchy_distribution;
#include <boost/test/included/test_exec_monitor.hpp> // Boost.Test
#include <boost/test/floating_point_comparison.hpp>
#include <iostream>
using std::cout;
using std::endl;
using std::setprecision;
template <class RealType>
void test_spots(RealType T)
{
// Basic sanity checks.
// 50eps as a persentage, up to a maximum of double precision
// (that's the limit of our test data).
RealType tolerance = (std::max)(
static_cast<RealType>(boost::math::tools::epsilon<double>()),
boost::math::tools::epsilon<RealType>());
tolerance *= 50 * 100;
cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl;
//
// CDF:
//
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.125)), // x
static_cast<RealType>(0.53958342416056554201085167134004L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-0.125)), // x
static_cast<RealType>(0.46041657583943445798914832865996L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(0.64758361765043327417540107622474L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-0.5)), // x
static_cast<RealType>(0.35241638234956672582459892377526), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(1.0)), // x
static_cast<RealType>(0.75), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-1.0)), // x
static_cast<RealType>(0.25), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(2.0)), // x
static_cast<RealType>(0.85241638234956672582459892377526L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-2.0)), // x
static_cast<RealType>(0.14758361765043327417540107622474L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(10.0)), // x
static_cast<RealType>(0.9682744825694464304850228813987L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-10.0)), // x
static_cast<RealType>(0.031725517430553569514977118601302L), // probability.
tolerance); // %
//
// Complements:
//
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.125))), // x
static_cast<RealType>(0.46041657583943445798914832865996L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(-0.125))), // x
static_cast<RealType>(0.53958342416056554201085167134004L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.5))), // x
static_cast<RealType>(0.35241638234956672582459892377526L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(-0.5))), // x
static_cast<RealType>(0.64758361765043327417540107622474L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(1.0))), // x
static_cast<RealType>(0.25), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(-1.0))), // x
static_cast<RealType>(0.75), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(2.0))), // x
static_cast<RealType>(0.14758361765043327417540107622474L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(-2.0))), // x
static_cast<RealType>(0.85241638234956672582459892377526L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(10.0))), // x
static_cast<RealType>(0.031725517430553569514977118601302L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(-10.0))), // x
static_cast<RealType>(0.9682744825694464304850228813987L), // probability.
tolerance); // %
//
// Quantiles:
//
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.53958342416056554201085167134004L)),
static_cast<RealType>(0.125),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.46041657583943445798914832865996L)),
static_cast<RealType>(-0.125),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.64758361765043327417540107622474L)),
static_cast<RealType>(0.5),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.35241638234956672582459892377526)),
static_cast<RealType>(-0.5),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.75)),
static_cast<RealType>(1.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.25)),
static_cast<RealType>(-1.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.85241638234956672582459892377526L)),
static_cast<RealType>(2.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.14758361765043327417540107622474L)),
static_cast<RealType>(-2.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.9682744825694464304850228813987L)),
static_cast<RealType>(10.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.031725517430553569514977118601302L)),
static_cast<RealType>(-10.0),
tolerance); // %
//
// Quantile from complement:
//
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.46041657583943445798914832865996L))),
static_cast<RealType>(0.125),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.53958342416056554201085167134004L))),
static_cast<RealType>(-0.125),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.35241638234956672582459892377526L))),
static_cast<RealType>(0.5),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.64758361765043327417540107622474L))),
static_cast<RealType>(-0.5),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.25))),
static_cast<RealType>(1.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.75))),
static_cast<RealType>(-1.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.14758361765043327417540107622474L))),
static_cast<RealType>(2.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.85241638234956672582459892377526L))),
static_cast<RealType>(-2.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.031725517430553569514977118601302L))),
static_cast<RealType>(10.0),
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(cauchy_distribution<RealType>(),
static_cast<RealType>(0.9682744825694464304850228813987L))),
static_cast<RealType>(-10.0),
tolerance); // %
//
// PDF
//
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.125)), // x
static_cast<RealType>(0.31341281101173235351410956479511L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-0.125)), // x
static_cast<RealType>(0.31341281101173235351410956479511L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(0.25464790894703253723021402139602L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-0.5)), // x
static_cast<RealType>(0.25464790894703253723021402139602L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(1.0)), // x
static_cast<RealType>(0.15915494309189533576888376337251L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-1.0)), // x
static_cast<RealType>(0.15915494309189533576888376337251L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(2.0)), // x
static_cast<RealType>(0.063661977236758134307553505349006L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-2.0)), // x
static_cast<RealType>(0.063661977236758134307553505349006L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(10.0)), // x
static_cast<RealType>(0.0031515830315226799162155200667825L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(),
static_cast<RealType>(-10.0)), // x
static_cast<RealType>(0.0031515830315226799162155200667825L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(2, 5),
static_cast<RealType>(1)), // x
static_cast<RealType>(0.061213439650728975295724524374044L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::pdf(
cauchy_distribution<RealType>(-2, 0.25),
static_cast<RealType>(1)), // x
static_cast<RealType>(0.0087809623774838805941453110826215L), // probability.
tolerance); // %
//
// The following test values were calculated using MathCad,
// precision seems to be about 10^-13.
//
tolerance = (std::max)(tolerance, static_cast<RealType>(1e-11));
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(1, 1),
static_cast<RealType>(0.125)), // x
static_cast<RealType>(0.271189304634946L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(0.125)), // x
static_cast<RealType>(0.539583424160566L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(0.647583617650433L), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(1)), // x
static_cast<RealType>(0.750000000000000), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(2)), // x
static_cast<RealType>(0.852416382349567), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(10)), // x
static_cast<RealType>(0.968274482569447), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(100)), // x
static_cast<RealType>(0.996817007235092), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-0.125)), // x
static_cast<RealType>(0.460416575839434), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-0.5)), // x
static_cast<RealType>(0.352416382349567), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-1)), // x
static_cast<RealType>(0.2500000000000000), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-2)), // x
static_cast<RealType>(0.147583617650433), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-10)), // x
static_cast<RealType>(0.031725517430554), // probability.
tolerance); // %
BOOST_CHECK_CLOSE(
::boost::math::cdf(
cauchy_distribution<RealType>(0, 1),
static_cast<RealType>(-100)), // x
static_cast<RealType>(3.18299276490824E-3), // probability.
tolerance); // %
//
// Things that are errors:
//
cauchy_distribution<RealType> dist;
BOOST_CHECK_THROW(
mean(dist),
std::domain_error);
BOOST_CHECK_EQUAL(
mode(dist),
static_cast<RealType>(0));
BOOST_CHECK_THROW(
variance(dist),
std::domain_error);
BOOST_CHECK_THROW(
standard_deviation(dist),
std::domain_error);
BOOST_CHECK_THROW(
kurtosis(dist),
std::domain_error);
BOOST_CHECK_THROW(
kurtosis_excess(dist),
std::domain_error);
BOOST_CHECK_THROW(
skewness(dist),
std::domain_error);
BOOST_CHECK_THROW(
quantile(dist, RealType(0.0)),
std::overflow_error);
BOOST_CHECK_THROW(
quantile(dist, RealType(1.0)),
std::overflow_error);
BOOST_CHECK_THROW(
quantile(complement(dist, RealType(0.0))),
std::overflow_error);
BOOST_CHECK_THROW(
quantile(complement(dist, RealType(1.0))),
std::overflow_error);
} // template <class RealType>void test_spots(RealType)
int test_main(int, char* [])
{
// 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(0x582))
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* [])
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