// test_arcsine_dist.cpp
// Copyright John Maddock 2014.
// Copyright Paul A. Bristow 2014.
// 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)
// Tests for the arcsine Distribution.
#include <pch.hpp> // Must be 1st include, and include_directory /libs/math/src/tr1/ is needed.
#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.
#endif
#include <boost/math/concepts/real_concept.hpp> // for real_concept.
using ::boost::math::concepts::real_concept;
#include <boost/math/tools/test.hpp> // for real_concept.
#include <boost/math/distributions/arcsine.hpp> // for arcsine_distribution.
using boost::math::arcsine_distribution;
#include <boost/math/constants/constants.hpp>
using boost::math::constants::one_div_root_two;
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
#include <cmath>
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;
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 arcsine_distribution<RealType, ignore_all_policy> ignore_error_arcsine;
// 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)
{
// Demonstrate output of PDF with infinity,
// but strin goutput from NaN is platform dependent, so can't use BOOST_CHECK.
if (std::numeric_limits<RealType>::has_infinity)
{
//std::cout << "pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = " << pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) << std::endl;
// Outputs: pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = 1.#QNAN
}
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(-2)))); // x < xmin
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(-2)))); // x < xmin
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(+2)))); // x > x_max
BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(+2)))); // x > x_max
// Mean
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-nan, 0))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(+nan, 0))));
if (std::numeric_limits<RealType>::has_infinity)
{
//BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity(), 0))));
// std::cout << "arcsine(-inf,+1) mean " << mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity())) << std::endl;
//BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(std::numeric_limits<RealType>::infinity(), 0))));
}
// NaN constructors.
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(2, nan))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, nan))));
BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, 2))));
// Variance
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(nan, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, nan))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, nan))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(0, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(static_cast<RealType>(1.7L), 0))));
BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, 0))));
// Skewness
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(nan, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(-1, nan))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(0, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(1, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(2, 0))));
BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(3, 0))));
// Kurtosis
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(nan, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(-1, nan))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(0, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(2, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(3, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(4, 0))));
// Kurtosis excess
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(nan, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(-1, nan))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(0, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(1, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(2, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(3, 0))));
BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(4, 0))));
} // has_quiet_NaN
//
BOOST_CHECK(boost::math::isfinite(mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon()))));
check_support<arcsine_distribution<RealType> >(arcsine_distribution<RealType>(0, 1));
} // ordinary floats.
} // template <class RealType> void test_ignore_policy(RealType)
template <class RealType>
RealType informax()
{ //! \return Infinity else max_value.
return ((std::numeric_limits<RealType>::has_infinity) ?
std::numeric_limits<RealType>::infinity() : boost::math::tools::max_value<RealType>());
}
template <class RealType>
void test_spot(
RealType a, // alpha a or lo or x_min
RealType b, // arcsine b or hi or x_maz
RealType x, // Probability
RealType P, // CDF of arcsine(a, b)
RealType Q, // Complement of CDF of arcsine (a, b)
RealType tol) // Test tolerance.
{
boost::math::arcsine_distribution<RealType> anarcsine(a, b);
BOOST_CHECK_CLOSE_FRACTION(cdf(anarcsine, x), P, tol);
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 that Q is free of error,
// (and similarly for Q).
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(anarcsine, x)), Q, tol);
if (x != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
quantile(anarcsine, P), x, tol);
}
else
{
// Just check quantile is very small:
if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent)
&& (boost::is_floating_point<RealType>::value))
{
// Limit where this is checked: if exponent range is very large we may
// run out of iterations in our root finding algorithm.
BOOST_CHECK(quantile(anarcsine, P) < boost::math::tools::epsilon<RealType>() * 10);
}
} // if k
if (x != 0)
{
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(anarcsine, Q)), x, tol * 10);
}
else
{ // Just check quantile is very small:
if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
{ // Limit where this is checked: if exponent range is very large we may
// run out of iterations in our root finding algorithm.
BOOST_CHECK(quantile(complement(anarcsine, Q)) < boost::math::tools::epsilon<RealType>() * 10);
}
} // if x
}
} // template <class RealType> void test_spot
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType)
{
// Basic sanity checks with 'known good' values.
// so set tolerance to a few eps expressed as a fraction, or
// few eps of type double expressed as a fraction,
// whichever is the larger.
RealType tolerance = (std::max)
(boost::math::tools::epsilon<RealType>(),
static_cast<RealType>(std::numeric_limits<double>::epsilon())); // 0 if real_concept.
RealType max_value = boost::math::tools::max_value<RealType>();
RealType epsilon = boost::math::tools::epsilon<RealType>();
//cout << "Boost::math::tools::epsilon = " << boost::math::tools::epsilon<RealType>() << endl;
//cout << "std::numeric_limits::epsilon = " << std::numeric_limits<RealType>::epsilon() << endl;
tolerance *= 2; // Note: NO * 100 because tolerance is a fraction, NOT %.
cout << "tolerance = " << tolerance << endl;
using boost::math::arcsine_distribution;
using ::boost::math::cdf;
using ::boost::math::pdf;
using ::boost::math::complement;
using ::boost::math::quantile;
// Basic sanity-check spot values.
// Test values from Wolfram alpha, for example:
// http://www.wolframalpha.com/input/?i=+N%5BPDF%5Barcsinedistribution%5B0%2C+1%5D%2C+0.5%5D%2C+50%5D
// N[PDF[arcsinedistribution[0, 1], 0.5], 50]
// 0.63661977236758134307553505349005744813783858296183
arcsine_distribution<RealType> arcsine_01; // (Our) Standard arcsine.
// Member functions.
BOOST_CHECK_EQUAL(arcsine_01.x_min(), 0);
BOOST_CHECK_EQUAL(arcsine_01.x_max(), 1);
// Derived functions.
BOOST_CHECK_EQUAL(mean(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(median(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(variance(arcsine_01), 0.125); // 1/8 = 0.125
BOOST_CHECK_CLOSE_FRACTION(standard_deviation(arcsine_01), one_div_root_two<double>() / 2, tolerance); // 1/ sqrt(s) = 0.35355339059327379
BOOST_CHECK_EQUAL(skewness(arcsine_01), 0); //
BOOST_CHECK_EQUAL(kurtosis_excess(arcsine_01), -1.5); // 3/2
BOOST_CHECK_EQUAL(support(arcsine_01).first, 0); //
BOOST_CHECK_EQUAL(range(arcsine_01).first, 0); //
BOOST_MATH_CHECK_THROW(mode(arcsine_01), std::domain_error); // Two modes at x_min and x_max, so throw instead.
// PDF
// pdf of x = 1/4 is same as reflected value at x = 3/4.
// N[PDF[arcsinedistribution[0, 1], 0.25], 50]
// N[PDF[arcsinedistribution[0, 1], 0.75], 50]
// 0.73510519389572273268176866441729258852984864048885
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000001), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000005), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance);
// Note loss of significance when x is near x_max.
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 8 * tolerance); // Less accurate.
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999995), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), 50000 * tolerance); // Much less accurate.
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999999), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), 100000 * tolerance);// Even less accurate.
// Extreme x.
if (std::numeric_limits<RealType>::has_infinity)
{ //
BOOST_CHECK_EQUAL(pdf(arcsine_01, 0), informax<RealType>()); //
BOOST_CHECK_EQUAL(pdf(arcsine_01, 1), informax<RealType>()); //
}
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, tolerance),
1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, static_cast<RealType>(1) - tolerance),
1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); //
// CDF
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000001), static_cast<RealType>(0.00063661987847092448418377367957384866092127786060574L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000005), static_cast<RealType>(0.0014235262731079289297302426454125318201831474507326L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.05), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.5), static_cast<RealType>(0.5L), tolerance); // Exact.
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.95), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), 2 * tolerance);
// Values near unity should use the cdf complemented for better accuracy,
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999995), static_cast<RealType>(0.99857647372689207107026975735458746817981685254927L), 100 * tolerance); // Less accurate.
BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999999), static_cast<RealType>(0.99936338012152907551581622632042615133907872213939L), 1000 * tolerance); // Less accurate.
// Complement CDF
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(1 - 0.00063661987847092448418377367957384866092127786060574L), 2 * tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(0.99936338012152907551581622632043L), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.05)), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.5)), static_cast<RealType>(0.5L), tolerance); // Exact.
// Some values near unity when complement is expected to be less accurate.
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.95)), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); // 2 for asin
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.999999)), static_cast<RealType>(1 - 0.99936338012152907551581622632042615133907872213939L), 1000000 * tolerance); // 10000 for asin, 1000000 for acos.
// Quantile.
// Check 1st, 2nd and 3rd quartiles.
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.25L)), static_cast<RealType>(0.14644660940672624L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.75L)), static_cast<RealType>(0.85355339059327373L), tolerance);
// N[CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.14356629312870627075094188477505571882161519989741
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), 0.05, tolerance);
// Quantile of complement.
// N[1-CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.85643370687129372924905811522494428117838480010259
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), 0.05, tolerance * 2);
// N[sin^2[0.75 * pi/2],50] == 0.85355339059327376220042218105242451964241796884424
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.25L))), static_cast<RealType>(0.85355339059327376220042218105242451964241796884424L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.5L))), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.75L))), static_cast<RealType>(0.14644660940672623779957781894757548035758203115576L), 2 * tolerance); // Less accurate.
// N[CDF[arcsinedistribution[0, 1], 0.25], 5
// 0.33333333333333333333333333333333333333333333333333
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(1) / 3), static_cast<RealType>(0.25L), 2 * tolerance);
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance); // probability = 0.5, x = 0.5
BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(2) / 3), static_cast<RealType>(0.75L), tolerance);
// Arcsine(-1, +1) xmin = -1, x_max = +1 symmetric about zero.
arcsine_distribution<RealType> as_m11(-1, +1);
BOOST_CHECK_EQUAL(as_m11.x_min(), -1); //
BOOST_CHECK_EQUAL(as_m11.x_max(), +1);
BOOST_CHECK_EQUAL(mean(as_m11), 0); //
BOOST_CHECK_EQUAL(median(as_m11), 0); //
BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as_m11), one_div_root_two<RealType>(), tolerance * 2); //
BOOST_CHECK_EQUAL(variance(as_m11), 0.5); // 1 - (-1) = 2 ^ 2 = 4 /8 = 0.5
BOOST_CHECK_EQUAL(skewness(as_m11), 0); //
BOOST_CHECK_EQUAL(kurtosis_excess(as_m11), -1.5); // 3/2
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.05), static_cast<RealType>(0.31870852113797122803869876869296281629727218095644L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.5), static_cast<RealType>(0.36755259694786136634088433220864629426492432024443L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.95), static_cast<RealType>(1.0194074882503562519812229448639426942621591013381L), 2 * tolerance); // Less accurate.
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.05), static_cast<RealType>(0.51592213323666034437274347433261364289389772737836L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.5), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), 2 * tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.95), static_cast<RealType>(0.89891737589574013042121018491729701360300248368629L), tolerance); // Not less accurate.
// Quantile
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(1) / 3), -static_cast<RealType>(0.5L), 2 * tolerance); // p = 1/3 x = -0.5
BOOST_CHECK_SMALL(quantile(as_m11, static_cast<RealType>(0.5L)), 2 * tolerance); // p = 0.5, x = 0
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(2) / 3), +static_cast<RealType>(0.5L), 4 * tolerance); // p = 2/3, x = +0.5
// Loop back tests.
test_spot(
static_cast<RealType>(0), // lo or a
static_cast<RealType>(1), // hi or b
static_cast<RealType>(0.05), // Random variate x
static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Probability of result (CDF of arcsine), P
static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(0), // lo or a
static_cast<RealType>(1), // hi or b
static_cast<RealType>(0.95), // Random variate x
static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Probability of result (CDF of arcsine), P
static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Complement of CDF Q = 1 - P
tolerance * 4); // Test tolerance (slightly inceased compared to x < 0.5 above).
test_spot(
static_cast<RealType>(0), // lo or a
static_cast<RealType>(1), // hi or b
static_cast<RealType>(static_cast<RealType>(0.5L)), // Random variate x
static_cast<RealType>(static_cast<RealType>(0.5L)), // Probability of result (CDF of arcsine), P
static_cast<RealType>(static_cast<RealType>(0.5L)), // Complement of CDF Q = 1 - P
tolerance * 4); // Test tolerance.
// Arcsine(-2, -1) xmin = -2, x_max = -1 - Asymmetric both negative.
arcsine_distribution<RealType> as_m2m1(-2, -1);
BOOST_CHECK_EQUAL(as_m2m1.x_min(), -2); //
BOOST_CHECK_EQUAL(as_m2m1.x_max(), -1);
BOOST_CHECK_EQUAL(mean(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(median(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(variance(as_m2m1), 0.125);
BOOST_CHECK_EQUAL(skewness(as_m2m1), 0); //
BOOST_CHECK_EQUAL(kurtosis_excess(as_m2m1), -1.5); // 3/2
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance); // Less accurate.
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.05), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.5), static_cast<RealType>(0.5L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.95), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); // Not much less accurate.
// Quantile
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L)), -static_cast<RealType>(1.05L), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), -static_cast<RealType>(1.95L), 4 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L))), -static_cast<RealType>(1.05L), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance); //
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), -static_cast<RealType>(1.95L), 4 * tolerance);
// Tests that should throw:
BOOST_MATH_CHECK_THROW(mode(arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1))), std::domain_error);
// mode is undefined, and must throw domain_error!
BOOST_MATH_CHECK_THROW( // For various bad arguments.
pdf(
arcsine_distribution<RealType>(static_cast<RealType>(+1), static_cast<RealType>(-1)), // min_x > max_x
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad constructor parameters.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad constructor parameters.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // equal constructor parameters.
static_cast<RealType>(-1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad x > 1.
static_cast<RealType>(999)), std::domain_error);
// Checks on things that are errors.
// Construction with 'bad' parameters.
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, -1), std::domain_error); // max < min.
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, 0), std::domain_error); // max < min.
arcsine_distribution<> dist;
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::domain_error);
BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
// Various combinations of bad contructor and member function parameters.
BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(0, 1), -1), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(-1, 1), +2), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), -1), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), 2), std::domain_error);
// No longer allow any parameter to be NaN or inf, so all these tests should throw.
if (std::numeric_limits<RealType>::has_quiet_NaN)
{
// Attempt to construct from non-finite parameters should throw.
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, nan), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan, 1), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, nan), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan, 1), std::domain_error);
#endif
arcsine_distribution<RealType> w(RealType(-1), RealType(+1));
// NaN parameters to member functions should throw.
BOOST_MATH_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN
BOOST_MATH_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN
BOOST_MATH_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan
BOOST_MATH_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan
BOOST_MATH_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan
} // has_quiet_NaN
if (std::numeric_limits<RealType>::has_infinity)
{
// Attempt to construct from non-finite should throw.
RealType inf = std::numeric_limits<RealType>::infinity();
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error);
#endif
// Infinite parameters to member functions should throw.
arcsine_distribution<RealType> w(RealType(0), RealType(1));
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error);
#endif
BOOST_MATH_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf
BOOST_MATH_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf
BOOST_MATH_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf
BOOST_MATH_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf
BOOST_MATH_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf
} // has_infinity
// Error handling checks:
check_out_of_range<boost::math::arcsine_distribution<RealType> >(-1, +1); // (All) valid constructor parameter values.
// and range and non-finite.
test_ignore_policy(static_cast<RealType>(0));
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE(test_main)
{
BOOST_MATH_CONTROL_FP;
// Check that can generate arcsine distribution using convenience method:
using boost::math::arcsine;
arcsine_distribution<> arcsine_01; // Using default RealType double.
// Note: NOT arcsine01() - or compiler will assume a function.
arcsine as; // Using typedef for default standard arcsine.
//
BOOST_CHECK_EQUAL(as.x_min(), 0); //
BOOST_CHECK_EQUAL(as.x_max(), 1);
BOOST_CHECK_EQUAL(mean(as), 0.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(median(as), 0.5); // 1 / (1 + 1) = 1/2 exactly.
BOOST_CHECK_EQUAL(variance(as), 0.125); //0.125
BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as), one_div_root_two<double>() / 2, std::numeric_limits<double>::epsilon()); // 0.353553
BOOST_CHECK_EQUAL(skewness(as), 0); //
BOOST_CHECK_EQUAL(kurtosis_excess(as), -1.5); // 3/2
BOOST_CHECK_EQUAL(support(as).first, 0); //
BOOST_CHECK_EQUAL(range(as).first, 0); //
BOOST_MATH_CHECK_THROW(mode(as), std::domain_error); // Two modes at x_min and x_max, so throw instead.
// (Parameter value, arbitrarily zero, only communicates the floating point type).
test_spots(0.0F); // Test float.
test_spots(0.0); // Test double.
#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
#endif
/* */
} // BOOST_AUTO_TEST_CASE( test_main )
/*
Microsoft Visual Studio Professional 2013
Version 12.0.30110.00 Update 1
1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
1> Running 1 test case...
1> Platform: Win32
1> Compiler: Microsoft Visual C++ version 12.0 ???? MSVC says 2013
1> STL : Dinkumware standard library version 610
1> Boost : 1.56.0
Sample Output is:
1> Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
1> Running 1 test case...
1> Platform: Win32
1> Compiler: Microsoft Visual C++ version 12.0
1> STL : Dinkumware standard library version 610
1> Boost : 1.56.0
1> tolerance = 2.38419e-007
1> tolerance = 4.44089e-016
1> tolerance = 4.44089e-016
1> tolerance = 4.44089e-016
1>
1> *** No errors detected
GCC 4.9.1
Running 1 test case...
tolerance = 2.38419e-007
tolerance = 4.44089e-016
tolerance = 4.44089e-016
tolerance = 4.44089e-016
*** No errors detected
RUN SUCCESSFUL (total time: 141ms)
*/