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Sleds/cppboost/libs/math/test/test_nc_t.cpp

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// test_nc_t.cpp
// Copyright John Maddock 2008, 2012.
// Copyright Paul A. Bristow 2012.
// 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)
#include <pch.hpp> // Need to include lib/math/test in path.
#ifdef _MSC_VER
#pragma warning (disable:4127 4512)
#endif
#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
# define TEST_FLOAT
# define TEST_DOUBLE
# define TEST_LDOUBLE
# define TEST_REAL_CONCEPT
#endif
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#include <boost/math/distributions/non_central_t.hpp> // for chi_squared_distribution.
#include <boost/math/distributions/normal.hpp> // for normal distribution (for comparison).
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/results_collector.hpp>
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;
#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
{\
unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
BOOST_CHECK_CLOSE(a, b, prec); \
if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
{\
std::cerr << "Failure was at row " << i << std::endl;\
std::cerr << std::setprecision(35); \
std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
}\
}
#define BOOST_CHECK_EX(a, i) \
{\
unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
BOOST_CHECK(a); \
if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
{\
std::cerr << "Failure was at row " << i << std::endl;\
std::cerr << std::setprecision(35); \
std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
}\
}
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double|real_concept";
}
else
{
largest_type = "long double|real_concept";
}
#else
largest_type = "(long\\s+)?double|real_concept";
#endif
//
// Catch all cases come last:
//
if(std::numeric_limits<long double>::digits > 54)
{
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 2000000, 200000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"double", // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 500, 100); // test function
}
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
"real_concept", // test type(s)
"[^|]*", // test data group
"[^|]*", 300000, 100000); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*large[^|]*", // test data group
"[^|]*", 1500, 300); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*small[^|]*", // test data group
"[^|]*", 400, 100); // test function
add_expected_result(
"[^|]*", // compiler
"[^|]*", // stdlib
"[^|]*", // platform
largest_type, // test type(s)
"[^|]*", // test data group
"[^|]*", 250, 50); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class RealType>
RealType naive_pdf(RealType v, RealType delta, RealType x)
{
}
template <class RealType>
RealType naive_mean(RealType v, RealType delta)
{
using boost::math::tgamma;
return delta * sqrt(v / 2) * tgamma((v-1)/2) / tgamma(v/2);
}
float naive_mean(float v, float delta)
{
return (float)naive_mean((double)v, (double)delta);
}
template <class RealType>
RealType naive_variance(RealType v, RealType delta)
{
using boost::math::tgamma;
RealType r = tgamma((v-1)/2) / tgamma(v/2);
r *= r;
r *= -delta * delta * v / 2;
r += (1 + delta * delta) * v / (v - 2);
return r;
}
float naive_variance(float v, float delta)
{
return (float)naive_variance((double)v, (double)delta);
}
template <class RealType>
RealType naive_skewness(RealType v, RealType delta)
{
using boost::math::tgamma;
RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
RealType r = delta * sqrt(v) * tgamma((v-1)/2)
* (v * (-3 + delta * delta + 2 * v) / ((-3 + v) * (-2 + v))
- 2 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2));
r /= boost::math::constants::root_two<RealType>()
* pow(((1+delta*delta) * v / (-2+v) - delta*delta*v*tgr*tgr/2), RealType(1.5f))
* tgamma(v/2);
return r;
}
float naive_skewness(float v, float delta)
{
return (float)naive_skewness((double)v, (double)delta);
}
template <class RealType>
RealType naive_kurtosis_excess(RealType v, RealType delta)
{
using boost::math::tgamma;
RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
RealType r = -delta * delta * v * tgr * tgr / 2;
r *= v * (delta * delta * (1 + v) + 3 * (-5 + 3 * v)) / ((-3 + v)*(-2+v))
- 3 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2);
r += (3 + 6 * delta * delta + delta * delta * delta * delta)* v * v
/ ((-4+v) * (-2+v));
r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
return r;
}
float naive_kurtosis_excess(float v, float delta)
{
return (float)naive_kurtosis_excess((double)v, (double)delta);
}
template <class RealType>
void test_spot(
RealType df, // Degrees of freedom
RealType ncp, // non-centrality param
RealType t, // T statistic
RealType P, // CDF
RealType Q, // Complement of CDF
RealType tol) // Test tolerance
{
boost::math::non_central_t_distribution<RealType> dist(df, ncp);
BOOST_CHECK_CLOSE(
cdf(dist, t), P, tol);
try{
BOOST_CHECK_CLOSE(
mean(dist), naive_mean(df, ncp), tol);
BOOST_CHECK_CLOSE(
variance(dist), naive_variance(df, ncp), tol);
BOOST_CHECK_CLOSE(
skewness(dist), naive_skewness(df, ncp), tol * 10);
BOOST_CHECK_CLOSE(
kurtosis_excess(dist), naive_kurtosis_excess(df, ncp), tol * 50);
BOOST_CHECK_CLOSE(
kurtosis(dist), 3 + naive_kurtosis_excess(df, ncp), tol * 50);
}
catch(const std::domain_error&)
{
}
/*
BOOST_CHECK_CLOSE(
pdf(dist, t), naive_pdf(dist.degrees_of_freedom(), ncp, t), tol * 50);
*/
if((P < 0.99) && (Q < 0.99))
{
//
// We can only check this if P is not too close to 1,
// so that we can guarantee Q is reasonably free of error:
//
BOOST_CHECK_CLOSE(
cdf(complement(dist, t)), Q, tol);
BOOST_CHECK_CLOSE(
quantile(dist, P), t, tol * 10);
BOOST_CHECK_CLOSE(
quantile(complement(dist, Q)), t, tol * 10);
/* Removed because can give more than one solution.
BOOST_CHECK_CLOSE(
dist.find_degrees_of_freedom(ncp, t, P), df, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_degrees_of_freedom(boost::math::complement(ncp, t, Q)), df, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_non_centrality(df, t, P), ncp, tol * 10);
BOOST_CHECK_CLOSE(
dist.find_non_centrality(boost::math::complement(df, t, Q)), ncp, tol * 10);
*/
}
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
//
// Approx limit of test data is 12 digits expressed here as a percentage:
//
RealType tolerance = (std::max)(
boost::math::tools::epsilon<RealType>(),
(RealType)5e-12f) * 100;
//
// At float precision we need to up the tolerance, since
// the input values are rounded off to inexact quantities
// the results get thrown off by a noticeable amount.
//
if(boost::math::tools::digits<RealType>() < 50)
tolerance *= 50;
if(boost::is_floating_point<RealType>::value != 1)
tolerance *= 20; // real_concept special functions are less accurate
cout << "Tolerance = " << tolerance << "%." << endl;
//
// Test data is taken from:
//
// Computing discrete mixtures of continuous
// distributions: noncentral chisquare, noncentral t
// and the distribution of the square of the sample
// multiple correlation coeficient.
// Denise Benton, K. Krishnamoorthy.
// Computational Statistics & Data Analysis 43 (2003) 249 - 267
//
test_spot(
static_cast<RealType>(3), // degrees of freedom
static_cast<RealType>(1), // non centrality
static_cast<RealType>(2.34), // T
static_cast<RealType>(0.801888999613917), // Probability of result (CDF), P
static_cast<RealType>(1-0.801888999613917), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(126), // degrees of freedom
static_cast<RealType>(-2), // non centrality
static_cast<RealType>(-4.33), // T
static_cast<RealType>(1.252846196792878e-2), // Probability of result (CDF), P
static_cast<RealType>(1-1.252846196792878e-2), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(20), // degrees of freedom
static_cast<RealType>(23), // non centrality
static_cast<RealType>(23), // T
static_cast<RealType>(0.460134400391924), // Probability of result (CDF), P
static_cast<RealType>(1-0.460134400391924), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(20), // degrees of freedom
static_cast<RealType>(33), // non centrality
static_cast<RealType>(34), // T
static_cast<RealType>(0.532008386378725), // Probability of result (CDF), P
static_cast<RealType>(1-0.532008386378725), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(12), // degrees of freedom
static_cast<RealType>(38), // non centrality
static_cast<RealType>(39), // T
static_cast<RealType>(0.495868184917805), // Probability of result (CDF), P
static_cast<RealType>(1-0.495868184917805), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(12), // degrees of freedom
static_cast<RealType>(39), // non centrality
static_cast<RealType>(39), // T
static_cast<RealType>(0.446304024668836), // Probability of result (CDF), P
static_cast<RealType>(1-0.446304024668836), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(200), // degrees of freedom
static_cast<RealType>(38), // non centrality
static_cast<RealType>(39), // T
static_cast<RealType>(0.666194209961795), // Probability of result (CDF), P
static_cast<RealType>(1-0.666194209961795), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(200), // degrees of freedom
static_cast<RealType>(42), // non centrality
static_cast<RealType>(40), // T
static_cast<RealType>(0.179292265426085), // Probability of result (CDF), P
static_cast<RealType>(1-0.179292265426085), // Q = 1 - P
tolerance);
/* This test fails
"Result of tgamma is too large to represent" at naive_mean check for max and infinity.
if (std::numeric_limits<RealType>::has_infinity)
{
test_spot(
//static_cast<RealType>(std::numeric_limits<RealType>::infinity()), // degrees of freedom
static_cast<RealType>((std::numeric_limits<RealType>::max)()), // degrees of freedom
static_cast<RealType>(10), // non centrality
static_cast<RealType>(11), // T
static_cast<RealType>(0.84134474606854293), // Probability of result (CDF), P
static_cast<RealType>(0.15865525393145707), // Q = 1 - P
tolerance);
}
*/
boost::math::non_central_t_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(12));
BOOST_CHECK_CLOSE(pdf(dist, 12), static_cast<RealType>(1.235329715425894935157684607751972713457e-1L), tolerance);
BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution<RealType>(126, -2), -4), static_cast<RealType>(5.797932289365814702402873546466798025787e-2L), tolerance);
BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution<RealType>(126, 2), 4), static_cast<RealType>(5.797932289365814702402873546466798025787e-2L), tolerance);
BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution<RealType>(126, 2), 0), static_cast<RealType>(5.388394890639957139696546086044839573749e-2L), tolerance);
// Error handling checks:
//check_out_of_range<boost::math::non_central_t_distribution<RealType> >(1, 1); // Fails one check because df for this distribution *can* be infinity.
BOOST_CHECK_THROW(pdf(boost::math::non_central_t_distribution<RealType>(0, 1), 0), std::domain_error);
BOOST_CHECK_THROW(pdf(boost::math::non_central_t_distribution<RealType>(-1, 1), 0), std::domain_error);
BOOST_CHECK_THROW(quantile(boost::math::non_central_t_distribution<RealType>(1, 1), -1), std::domain_error);
BOOST_CHECK_THROW(quantile(boost::math::non_central_t_distribution<RealType>(1, 1), 2), std::domain_error);
} // template <class RealType>void test_spots(RealType)
template <class T>
T nct_cdf(T df, T nc, T x)
{
return cdf(boost::math::non_central_t_distribution<T>(df, nc), x);
}
template <class T>
T nct_ccdf(T df, T nc, T x)
{
return cdf(complement(boost::math::non_central_t_distribution<T>(df, nc), x));
}
template <typename Real, typename T>
void do_test_nc_t(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef Real value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp1)(value_type, value_type, value_type) = nct_cdf;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp1, 0, 1, 2),
extract_result<Real>(3));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "CDF", test);
fp1 = nct_ccdf;
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(fp1, 0, 1, 2),
extract_result<Real>(4));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "CCDF", test);
std::cout << std::endl;
}
template <typename Real, typename T>
void quantile_sanity_check(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef Real value_type;
//
// Tests with type real_concept take rather too long to run, so
// for now we'll disable them:
//
if(!boost::is_floating_point<value_type>::value)
return;
std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
//
// These sanity checks test for a round trip accuracy of one half
// of the bits in T, unless T is type float, in which case we check
// for just one decimal digit. The problem here is the sensitivity
// of the functions, not their accuracy. This test data was generated
// for the forward functions, which means that when it is used as
// the input to the inverses then it is necessarily inexact. This rounding
// of the input is what makes the data unsuitable for use as an accuracy check,
// and also demonstrates that you can't in general round-trip these functions.
// It is however a useful sanity check.
//
value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float
for(unsigned i = 0; i < data.size(); ++i)
{
if(data[i][3] == 0)
{
BOOST_CHECK(0 == quantile(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), data[i][3]));
}
else if(data[i][3] < 0.9999f)
{
value_type p = quantile(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), data[i][3]);
value_type pt = data[i][2];
BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
}
if(data[i][4] == 0)
{
BOOST_CHECK(0 == quantile(complement(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), data[i][3])));
}
else if(data[i][4] < 0.9999f)
{
value_type p = quantile(complement(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), data[i][4]));
value_type pt = data[i][2];
BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
}
if(boost::math::tools::digits<value_type>() > 50)
{
//
// Sanity check mode, the accuracy of
// the mode is at *best* the square root of the accuracy of the PDF:
//
try{
value_type m = mode(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]));
value_type p = pdf(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), m);
value_type delta = (std::max)(fabs(m * sqrt(precision) * 50), sqrt(precision) * 50);
BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), m + delta) <= p, i);
BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution<value_type>(data[i][0], data[i][1]), m - delta) <= p, i);
}
catch(const boost::math::evaluation_error& ) {}
#if 0
//
// Sanity check degrees-of-freedom finder, don't bother at float
// precision though as there's not enough data in the probability
// values to get back to the correct degrees of freedom or
// non-centrality parameter:
//
try{
if((data[i][3] < 0.99) && (data[i][3] != 0))
{
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_t_distribution<value_type>::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
data[i][0], precision, i);
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_t_distribution<value_type>::find_non_centrality(data[i][0], data[i][2], data[i][3]),
data[i][1], precision, i);
}
if((data[i][4] < 0.99) && (data[i][4] != 0))
{
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_t_distribution<value_type>::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
data[i][0], precision, i);
BOOST_CHECK_CLOSE_EX(
boost::math::non_central_t_distribution<value_type>::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
data[i][1], precision, i);
}
}
catch(const std::exception& e)
{
BOOST_ERROR(e.what());
}
#endif
}
}
}
template <typename T>
void test_accuracy(T, const char* type_name)
{
#include "nct.ipp"
do_test_nc_t<T>(nct, type_name, "Non Central T");
quantile_sanity_check<T>(nct, type_name, "Non Central T");
if(std::numeric_limits<T>::is_specialized)
{
//
// Don't run these tests for real_concept: they take too long and don't converge
// without numeric_limits and lanczos support:
//
#include "nct_small_delta.ipp"
do_test_nc_t<T>(nct_small_delta, type_name, "Non Central T (small non-centrality)");
quantile_sanity_check<T>(nct_small_delta, type_name, "Non Central T (small non-centrality)");
#include "nct_asym.ipp"
do_test_nc_t<T>(nct_asym, type_name, "Non Central T (large parameters)");
quantile_sanity_check<T>(nct_asym, type_name, "Non Central T (large parameters)");
}
}
template <class RealType>
void test_big_df(RealType)
{
using namespace boost::math;
if (typeid(RealType) != typeid(boost::math::concepts::real_concept))
{ // Ordinary floats only.
// Could also test if (std::numeric_limits<RealType>::is_specialized);
RealType tolerance = 10 * boost::math::tools::epsilon<RealType>(); // static_cast<RealType>(1e-14); //
std::cout.precision(17); // Note: need to reset after calling BOOST_CHECK_s
// due to buglet in Boost.test that fails to restore precision corrrectly.
// Test for large degrees of freedom when should be same as normal.
RealType inf =
(std::numeric_limits<RealType>::has_infinity) ?
std::numeric_limits<RealType>::infinity()
:
boost::math::tools::max_value<RealType>();
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
// Tests for df = max_value and infinity.
RealType max_val = boost::math::tools::max_value<RealType>();
non_central_t_distribution<RealType> maxdf(max_val, 0);
BOOST_CHECK_EQUAL(maxdf.degrees_of_freedom(), max_val);
non_central_t_distribution<RealType> infdf(inf, 0);
BOOST_CHECK_EQUAL(infdf.degrees_of_freedom(), inf);
BOOST_CHECK_EQUAL(mean(infdf), 0);
BOOST_CHECK_EQUAL(mean(maxdf), 0);
BOOST_CHECK_EQUAL(variance(infdf), 1);
BOOST_CHECK_EQUAL(variance(maxdf), 1);
BOOST_CHECK_EQUAL(skewness(infdf), 0);
BOOST_CHECK_EQUAL(skewness(maxdf), 0);
BOOST_CHECK_EQUAL(kurtosis_excess(infdf), 3);
BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(maxdf), static_cast<RealType>(3), tolerance);
// Bad df examples.
BOOST_CHECK_THROW(non_central_t_distribution<RealType> minfdf(-inf, 0), std::domain_error);
BOOST_CHECK_THROW(non_central_t_distribution<RealType> minfdf(nan, 0), std::domain_error);
BOOST_CHECK_THROW(non_central_t_distribution<RealType> minfdf(-nan, 0), std::domain_error);
// BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0), static_cast<RealType>(0.3989422804014326779399460599343818684759L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(maxdf, 0), boost::math::constants::one_div_root_two_pi<RealType>() , tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0), boost::math::constants::one_div_root_two_pi<RealType>() , tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(infdf, 0), boost::math::constants::half<RealType>() , tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(maxdf, 0), boost::math::constants::half<RealType>() , tolerance);
// non-centrality delta = 10
// Degrees of freedom = Max value and = infinity should be very close.
non_central_t_distribution<RealType> maxdf10(max_val, 10);
non_central_t_distribution<RealType> infdf10(inf, 10);
BOOST_CHECK_EQUAL(infdf10.degrees_of_freedom(), inf);
BOOST_CHECK_EQUAL(infdf10.non_centrality(), 10);
BOOST_CHECK_EQUAL(mean(infdf10), 10);
BOOST_CHECK_CLOSE_FRACTION(mean(maxdf10), static_cast<RealType>(10), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(infdf10, 11), pdf(maxdf10, 11), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(infdf10, 11)), 1 - cdf(infdf10, 11), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(maxdf10, 11)), 1 - cdf(maxdf10, 11), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(infdf10, 11)), 1 - cdf(maxdf10, 11), tolerance); //
std::cout.precision(17);
//std::cout << "cdf(maxdf10, 11) = " << cdf(maxdf10, 11) << ' ' << cdf(complement(maxdf10, 11)) << endl;
//std::cout << "cdf(infdf10, 11) = " << cdf(infdf10, 11) << ' ' << cdf(complement(infdf10, 11)) << endl;
//std::cout << "quantile(maxdf10, 0.5) = " << quantile(maxdf10, 0.5) << std::endl; // quantile(maxdf10, 0.5) = 10.000000000000004
//std::cout << "quantile(infdf10, 0.5) = " << ' ' << quantile(infdf10, 0.5) << std::endl; // quantile(infdf10, 0.5) = 10
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.5), static_cast<RealType>(10), tolerance);
BOOST_CHECK_CLOSE_FRACTION(quantile(maxdf10, 0.5), static_cast<RealType>(10), tolerance);
BOOST_TEST_MESSAGE("non_central_t_distribution<RealType> infdf100(inf, 100);");
non_central_t_distribution<RealType> infdf100(inf, 100);
BOOST_TEST_MESSAGE("non_central_t_distribution<RealType> maxdf100(max_val, 100);");
non_central_t_distribution<RealType> maxdf100(max_val, 100);
BOOST_TEST_MESSAGE("BOOST_CHECK_CLOSE_FRACTION(quantile(infdf100, 0.5), static_cast<RealType>(100), tolerance);");
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf100, 0.5), static_cast<RealType>(100), tolerance);
BOOST_TEST_MESSAGE("BOOST_CHECK_CLOSE_FRACTION(quantile(maxdf100, 0.5), static_cast<RealType>(100), tolerance);");
BOOST_CHECK_CLOSE_FRACTION(quantile(maxdf100, 0.5), static_cast<RealType>(100), tolerance);
{ // Loop back.
RealType p = static_cast<RealType>(0.01);
RealType x = quantile(infdf10, p);
RealType c = cdf(infdf10, x);
BOOST_CHECK_CLOSE_FRACTION(c, p, tolerance);
}
{
RealType q = static_cast<RealType>(0.99);
RealType x = quantile(complement(infdf10, q));
RealType c = cdf(complement(infdf10, x));
BOOST_CHECK_CLOSE_FRACTION(c, q, tolerance);
}
{ // Loop back.
RealType p = static_cast<RealType>(0.99);
RealType x = quantile(infdf10, p);
RealType c = cdf(infdf10, x);
BOOST_CHECK_CLOSE_FRACTION(c, p, tolerance);
}
{
RealType q = static_cast<RealType>(0.01);
RealType x = quantile(complement(infdf10, q));
RealType c = cdf(complement(infdf10, x));
BOOST_CHECK_CLOSE_FRACTION(c, q, tolerance *2); // c{0.0100000128} and q{0.00999999978}
}
//RealType cinf = quantile(infdf10, 0.25);
//std::cout << cinf << ' ' << cdf(infdf10, cinf) << std::endl; // 9.32551 0.25
//RealType cmax = quantile(maxdf10, 0.25);
//std::cout << cmax << ' ' << cdf(maxdf10, cmax) << std::endl; // 9.32551 0.25
//RealType cinfc = quantile(complement(infdf10, 0.75));
//std::cout << cinfc << ' ' << cdf(infdf10, cinfc) << std::endl; // 9.32551 0.25
//RealType cmaxc = quantile(complement(maxdf10, 0.75));
//std::cout << cmaxc << ' ' << cdf(maxdf10, cmaxc) << std::endl; // 9.32551 0.25
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.5), quantile(maxdf10, 0.5), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.2), quantile(maxdf10, 0.2), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.8), quantile(maxdf10, 0.8), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.25), quantile(complement(infdf10, 0.75)), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(infdf10, 0.5)), quantile(complement(maxdf10, 0.5)), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(maxdf10, 0.25), quantile(complement(maxdf10, 0.75)), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.99), quantile(complement(infdf10, 0.01)), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.4), quantile(complement(infdf10, 0.6)), tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(infdf10, 0.01), quantile(complement(infdf10, 1 - 0.01)), tolerance); //
}
} // void test_big_df(RealType)
template <class RealType>
void test_ignore_policy(RealType)
{
// Check on returns when errors are ignored.
if ((typeid(RealType) != typeid(boost::math::concepts::real_concept))
&& std::numeric_limits<RealType>::has_infinity
&& std::numeric_limits<RealType>::has_quiet_NaN
)
{ // Ordinary floats only.
using namespace boost::math;
// RealType inf = std::numeric_limits<RealType>::infinity();
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
using boost::math::policies::policy;
// Types of error whose action can be altered by policies:.
//using boost::math::policies::evaluation_error;
//using boost::math::policies::domain_error;
//using boost::math::policies::overflow_error;
//using boost::math::policies::underflow_error;
//using boost::math::policies::domain_error;
//using boost::math::policies::pole_error;
//// Actions on error (in enum error_policy_type):
//using boost::math::policies::errno_on_error;
//using boost::math::policies::ignore_error;
//using boost::math::policies::throw_on_error;
//using boost::math::policies::denorm_error;
//using boost::math::policies::pole_error;
//using boost::math::policies::user_error;
typedef policy<
boost::math::policies::domain_error<boost::math::policies::ignore_error>,
boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
boost::math::policies::pole_error<boost::math::policies::ignore_error>,
boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
> ignore_all_policy;
typedef non_central_t_distribution<RealType, ignore_all_policy> ignore_error_non_central_t;
// Only test NaN and infinity if type has these features (realconcept returns zero).
// Integers are always converted to RealType,
// others requires static cast to RealType from long double.
if(std::numeric_limits<RealType>::has_quiet_NaN)
{
// Mean
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(-nan, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(+nan, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(-1, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(0, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(1, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(2, nan))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_non_central_t(nan, nan))));
BOOST_CHECK(boost::math::isfinite(mean(ignore_error_non_central_t(2, 0)))); // OK
// Variance
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(nan, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(1, nan))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(2, nan))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(-1, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(0, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(1, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(static_cast<RealType>(1.7L), 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_non_central_t(2, 0))));
// Skewness
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(std::numeric_limits<RealType>::quiet_NaN(), 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(-1, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(0, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(1, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(2, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_non_central_t(3, 0))));
// Kurtosis
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(std::numeric_limits<RealType>::quiet_NaN(), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(-1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(0, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(2, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(static_cast<RealType>(2.0001L), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(3, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_non_central_t(4, 0))));
// Kurtosis excess
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(std::numeric_limits<RealType>::quiet_NaN(), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(-1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(0, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(2, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(static_cast<RealType>(2.0001L), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(3, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_non_central_t(4, 0))));
} // has_quiet_NaN
BOOST_CHECK(boost::math::isfinite(mean(ignore_error_non_central_t(1 + std::numeric_limits<RealType>::epsilon(), 0))));
BOOST_CHECK(boost::math::isfinite(variance(ignore_error_non_central_t(2 + 2 * std::numeric_limits<RealType>::epsilon(), 0))));
BOOST_CHECK(boost::math::isfinite(variance(ignore_error_non_central_t(static_cast<RealType>(2.0001L), 0))));
BOOST_CHECK(boost::math::isfinite(variance(ignore_error_non_central_t(2 + 2 * std::numeric_limits<RealType>::epsilon(), 0))));
BOOST_CHECK(boost::math::isfinite(skewness(ignore_error_non_central_t(3 + 3 * std::numeric_limits<RealType>::epsilon(), 0))));
BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_non_central_t(4 + 4 * std::numeric_limits<RealType>::epsilon(), 0))));
BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_non_central_t(static_cast<RealType>(4.0001L), 0))));
// check_out_of_range<non_central_t_distribution<RealType> >(1, 0); // Fails one check because allows df = infinity.
check_support<non_central_t_distribution<RealType> >(non_central_t_distribution<RealType>(1, 0));
} // ordinary floats.
} // template <class RealType> void test_ignore_policy(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
BOOST_MATH_CONTROL_FP;
// Basic sanity-check spot values.
expected_results();
// (Parameter value, arbitrarily zero, only communicates the floating point type).
#ifdef TEST_FLOAT
test_spots(0.0F); // Test float.
#endif
#ifdef TEST_DOUBLE
test_spots(0.0); // Test double.
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
test_spots(0.0L); // Test long double.
#endif
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#ifdef TEST_REAL_CONCEPT
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
#endif
#endif
#endif
#ifdef TEST_FLOAT
test_accuracy(0.0F, "float"); // Test float.
#endif
#ifdef TEST_DOUBLE
test_accuracy(0.0, "double"); // Test double.
#endif
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
#ifdef TEST_LDOUBLE
test_accuracy(0.0L, "long double"); // Test long double.
#endif
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#ifdef TEST_REAL_CONCEPT
test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
#endif
#endif
#endif
/* */
test_ignore_policy(0.0);
test_big_df(0.F); // float
test_big_df(0.); // double
} // BOOST_AUTO_TEST_CASE( test_main )
/*
Output:
Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_nc_t.exe"
Running 1 test case...
Tests run with Microsoft Visual C++ version 10.0, Dinkumware standard library version 520, Win32
Tolerance = 0.000596046%.
Tolerance = 5e-010%.
Tolerance = 5e-010%.
Tolerance = 1e-008%.
Testing: Non Central T
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<double> Max = 137.7 RMS Mean=31.5
worst case at row: 181
{ 188.01481628417969, -282.022216796875, -298.02532958984375, 0.1552789395983287, 0.84472106040167128 }
CCDF<double> Max = 150.4 RMS Mean=32.32
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
Testing: double quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<double> Max = 3.605 RMS Mean=1.031
worst case at row: 42
{ 7376104448, 7.3761043495323975e-007, -1.3614851236343384, 0.086680099352107118, 0.91331990064789292 }
CCDF<double> Max = 5.207 RMS Mean=1.432
worst case at row: 38
{ 1524088576, 1.5240885886669275e-007, 1.3784774541854858, 0.91597201432644526, 0.084027985673554725 }
Testing: double quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<double> Max = 286.4 RMS Mean=62.79
worst case at row: 24
{ 1.3091821180254421e+019, 1309.18212890625, 1308.01171875, 0.12091797523015677, 0.87908202476984321 }
CCDF<double> Max = 226.9 RMS Mean=50.41
worst case at row: 23
{ 7.9217674231144776e+018, 792.1767578125, 793.54827880859375, 0.91489369852628, 0.085106301473719961 }
Testing: double quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<long double> Max = 137.7 RMS Mean=31.5
worst case at row: 181
{ 188.01481628417969, -282.022216796875, -298.02532958984375, 0.1552789395983287, 0.84472106040167128 }
CCDF<long double> Max = 150.4 RMS Mean=32.32
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
Testing: long double quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<long double> Max = 3.605 RMS Mean=1.031
worst case at row: 42
{ 7376104448, 7.3761043495323975e-007, -1.3614851236343384, 0.086680099352107118, 0.91331990064789292 }
CCDF<long double> Max = 5.207 RMS Mean=1.432
worst case at row: 38
{ 1524088576, 1.5240885886669275e-007, 1.3784774541854858, 0.91597201432644526, 0.084027985673554725 }
Testing: long double quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<long double> Max = 286.4 RMS Mean=62.79
worst case at row: 24
{ 1.3091821180254421e+019, 1309.18212890625, 1308.01171875, 0.12091797523015677, 0.87908202476984321 }
CCDF<long double> Max = 226.9 RMS Mean=50.41
worst case at row: 23
{ 7.9217674231144776e+018, 792.1767578125, 793.54827880859375, 0.91489369852628, 0.085106301473719961 }
Testing: long double quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<real_concept> Max = 2.816e+005 RMS Mean=2.029e+004
worst case at row: 185
{ 191.50137329101562, -957.5068359375, -1035.4078369140625, 0.072545502958829097, 0.92745449704117089 }
CCDF<real_concept> Max = 1.304e+005 RMS Mean=1.529e+004
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
cdf(n10, 11) = 0.84134471416473389 0.15865525603294373
cdf(n10, 9) = 0.15865525603294373 0.84134471416473389
cdf(maxdf10, 11) = 0.84134477376937866 0.15865525603294373
cdf(infdf10, 11) = 0.84134477376937866 0.15865525603294373
cdf(n10, 11) = 0.84134474606854293 0.15865525393145707
cdf(n10, 9) = 0.15865525393145707 0.84134474606854293
cdf(maxdf10, 11) = 0.84134474606854293 0.15865525393145707
cdf(infdf10, 11) = 0.84134474606854293 0.15865525393145707
*** No errors detected
Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_nc_t.exe"
Running 1 test case...
Tests run with Microsoft Visual C++ version 10.0, Dinkumware standard library version 520, Win32
Tolerance = 0.000596046%.
Tolerance = 5e-010%.
Tolerance = 5e-010%.
Tolerance = 1e-008%.
Testing: Non Central T
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<float> Max = 0 RMS Mean=0
CCDF<float> Max = 0 RMS Mean=0
Testing: float quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<double> Max = 137.7 RMS Mean=31.5
worst case at row: 181
{ 188.01481628417969, -282.022216796875, -298.02532958984375, 0.1552789395983287, 0.84472106040167128 }
CCDF<double> Max = 150.4 RMS Mean=32.32
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
Testing: double quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<double> Max = 3.605 RMS Mean=1.031
worst case at row: 42
{ 7376104448, 7.3761043495323975e-007, -1.3614851236343384, 0.086680099352107118, 0.91331990064789292 }
CCDF<double> Max = 5.207 RMS Mean=1.432
worst case at row: 38
{ 1524088576, 1.5240885886669275e-007, 1.3784774541854858, 0.91597201432644526, 0.084027985673554725 }
Testing: double quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<double> Max = 286.4 RMS Mean=62.79
worst case at row: 24
{ 1.3091821180254421e+019, 1309.18212890625, 1308.01171875, 0.12091797523015677, 0.87908202476984321 }
CCDF<double> Max = 226.9 RMS Mean=50.41
worst case at row: 23
{ 7.9217674231144776e+018, 792.1767578125, 793.54827880859375, 0.91489369852628, 0.085106301473719961 }
Testing: double quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<long double> Max = 137.7 RMS Mean=31.5
worst case at row: 181
{ 188.01481628417969, -282.022216796875, -298.02532958984375, 0.1552789395983287, 0.84472106040167128 }
CCDF<long double> Max = 150.4 RMS Mean=32.32
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
Testing: long double quantile sanity check, with tests Non Central T
Testing: Non Central T (small non-centrality)
CDF<long double> Max = 3.605 RMS Mean=1.031
worst case at row: 42
{ 7376104448, 7.3761043495323975e-007, -1.3614851236343384, 0.086680099352107118, 0.91331990064789292 }
CCDF<long double> Max = 5.207 RMS Mean=1.432
worst case at row: 38
{ 1524088576, 1.5240885886669275e-007, 1.3784774541854858, 0.91597201432644526, 0.084027985673554725 }
Testing: long double quantile sanity check, with tests Non Central T (small non-centrality)
Testing: Non Central T (large parameters)
CDF<long double> Max = 286.4 RMS Mean=62.79
worst case at row: 24
{ 1.3091821180254421e+019, 1309.18212890625, 1308.01171875, 0.12091797523015677, 0.87908202476984321 }
CCDF<long double> Max = 226.9 RMS Mean=50.41
worst case at row: 23
{ 7.9217674231144776e+018, 792.1767578125, 793.54827880859375, 0.91489369852628, 0.085106301473719961 }
Testing: long double quantile sanity check, with tests Non Central T (large parameters)
Testing: Non Central T
CDF<real_concept> Max = 2.816e+005 RMS Mean=2.029e+004
worst case at row: 185
{ 191.50137329101562, -957.5068359375, -1035.4078369140625, 0.072545502958829097, 0.92745449704117089 }
CCDF<real_concept> Max = 1.304e+005 RMS Mean=1.529e+004
worst case at row: 184
{ 191.43339538574219, 765.73358154296875, 820.14422607421875, 0.89943076553533785, 0.10056923446466212 }
*** No errors detected
*/
/*
Temporary stuff from student's t version.
// Calculate 1 / eps, the point where student's t should change to normal distribution.
RealType limit = 1 / boost::math::tools::epsilon<RealType>();
using namespace boost::math::policies;
typedef policy<digits10<17> > accurate_policy; // 17 = max_digits10 where available.
limit = 1 / policies::get_epsilon<RealType, accurate_policy>();
BOOST_CHECK_CLOSE_FRACTION(limit, static_cast<RealType>(1) / std::numeric_limits<RealType>::epsilon(), tolerance);
// Default policy to get full accuracy.
// std::cout << "Switch over to normal if df > " << limit << std::endl;
// float Switch over to normal if df > 8.38861e+006
// double Switch over to normal if df > 4.5036e+015
// Can't test real_concept - doesn't converge.
boost::math::normal_distribution<RealType> n01(0, 1); //
boost::math::normal_distribution<RealType> n10(10, 1); //
non_central_t_distribution<RealType> nct(boost::math::tools::max_value<RealType>(), 0); // Well over the switchover point,
non_central_t_distribution<RealType> nct2(limit /5, 0); // Just below the switchover point,
non_central_t_distribution<RealType> nct3(limit /100, 0); // Well below the switchover point,
non_central_t_distribution<RealType> nct4(limit, 10); // Well below the switchover point, and 10 non-centrality.
// PDF
BOOST_CHECK_CLOSE_FRACTION(pdf(nct, 0), pdf(n01, 0.), tolerance); // normal and non-central t should be nearly equal.
BOOST_CHECK_CLOSE_FRACTION(pdf(nct2, 0), pdf(n01, 0.), tolerance); // should be very close to normal.
BOOST_CHECK_CLOSE_FRACTION(pdf(nct3, 0), pdf(n01, 0.), tolerance * 10); // should be close to normal.
// BOOST_CHECK_CLOSE_FRACTION(pdf(nct4, 10), pdf(n10, 0.), tolerance * 100); // should be fairly close to normal tolerance.
RealType delta = 10; // non-centrality.
RealType nu = static_cast<RealType>(limit); // df
boost::math::normal_distribution<RealType> nl(delta, 1); // Normal distribution that nct tends to for big df.
non_central_t_distribution<RealType> nct5(nu, delta); //
RealType x = delta;
// BOOST_CHECK_CLOSE_FRACTION(pdf(nct5, x), pdf(nl, x), tolerance * 10 ); // nu = 1e15
// BOOST_CHECK_CLOSE_FRACTION(pdf(nct5, x), pdf(nl, x), tolerance * 1000 ); // nu = 1e14
// BOOST_CHECK_CLOSE_FRACTION(pdf(nct5, x), pdf(nl, x), tolerance * 10000 ); // nu = 1e13
// BOOST_CHECK_CLOSE_FRACTION(pdf(nct5, x), pdf(nl, x), tolerance * 100000 ); // nu = 1e12
BOOST_CHECK_CLOSE_FRACTION(pdf(nct5, x), pdf(nl, x), tolerance * 5 ); // nu = 1/eps
// Increasing the non-centrality delta increases the difference too because increases asymmetry.
// For example, with non-centrality = 100, need tolerance * 500
// CDF
BOOST_CHECK_CLOSE_FRACTION(cdf(nct, 0), cdf(n01, 0.), tolerance); // should be exactly equal.
BOOST_CHECK_CLOSE_FRACTION(cdf(nct2, 0), cdf(n01, 0.), tolerance); // should be very close to normal.
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(n10, 11)), 1 - cdf(n10, 11), tolerance); //
// cdf(n10, 10) = 0.841345 0.158655
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(n10, 9)), 1 - cdf(n10, 9), tolerance); //
std::cout.precision(17);
std::cout << "cdf(n10, 11) = " << cdf(n10, 11) << ' ' << cdf(complement(n10, 11)) << endl;
std::cout << "cdf(n10, 9) = " << cdf(n10, 9) << ' ' << cdf(complement(n10, 9)) << endl;
std::cout << std::numeric_limits<double>::max_digits10 << std::endl;
std::cout.precision(17);
using boost::math::tools::max_value;
double eps = std::numeric_limits<double>::epsilon();
// Use policies so that if policy requests lower precision,
// then get the normal distribution approximation earlier.
//limit = static_cast<double>(1) / limit; // 1/eps
double delta = 1e2;
double df =
delta / (4 * eps);
std::cout << df << std::endl; // df = 1.125899906842624e+018
{
boost::math::non_central_t_distribution<double> dist(df, delta);
std::cout <<"mean " << mean(dist) << std::endl; // mean 1000
std::cout <<"variance " << variance(dist) << std::endl; // variance 1
std::cout <<"skewness " << skewness(dist) << std::endl; // skewness 8.8817841970012523e-010
std::cout <<"kurtosis_excess " << kurtosis_excess(dist) << std::endl; // kurtosis_excess 3.0001220703125
//1.125899906842624e+017
//mean 100
//variance 1
//skewness 8.8817841970012523e-012
//kurtosis_excess 3
}
*/
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