// test_beta_dist.cpp
// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009, 2010, 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)
// Basic sanity tests for the beta Distribution.
// http://members.aol.com/iandjmsmith/BETAEX.HTM beta distribution calculator
// Appreas to be a 64-bit calculator showing 17 decimal digit (last is noisy).
// Similar to mathCAD?
// http://www.nuhertz.com/statmat/distributions.html#Beta
// Pretty graphs and explanations for most distributions.
// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp
// provided 40 decimal digits accuracy incomplete beta aka beta regularized == cdf
// http://www.ausvet.com.au/pprev/content.php?page=PPscript
// mode 0.75 5/95% 0.9 alpha 7.39 beta 3.13
// http://www.epi.ucdavis.edu/diagnostictests/betabuster.html
// Beta Buster also calculates alpha and beta from mode & percentile estimates.
// This is NOT (yet) implemented.
#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>
#include <boost/math/distributions/beta.hpp> // for beta_distribution
using boost::math::beta_distribution;
using boost::math::beta;
#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 "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;
template <class RealType>
void test_spot(
RealType a, // alpha a
RealType b, // beta b
RealType x, // Probability
RealType P, // CDF of beta(a, b)
RealType Q, // Complement of CDF
RealType tol) // Test tolerance.
{
boost::math::beta_distribution<RealType> abeta(a, b);
BOOST_CHECK_CLOSE_FRACTION(cdf(abeta, 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(abeta, x)), Q, tol);
if(x != 0)
{
BOOST_CHECK_CLOSE_FRACTION(
quantile(abeta, 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(abeta, P) < boost::math::tools::epsilon<RealType>() * 10);
}
} // if k
if(x != 0)
{
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(abeta, Q)), 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(complement(abeta, Q)) < boost::math::tools::epsilon<RealType>() * 10);
}
} // if x
// Estimate alpha & beta from mean and variance:
BOOST_CHECK_CLOSE_FRACTION(
beta_distribution<RealType>::find_alpha(mean(abeta), variance(abeta)),
abeta.alpha(), tol);
BOOST_CHECK_CLOSE_FRACTION(
beta_distribution<RealType>::find_beta(mean(abeta), variance(abeta)),
abeta.beta(), tol);
// Estimate sample alpha and beta from others:
BOOST_CHECK_CLOSE_FRACTION(
beta_distribution<RealType>::find_alpha(abeta.beta(), x, P),
abeta.alpha(), tol);
BOOST_CHECK_CLOSE_FRACTION(
beta_distribution<RealType>::find_beta(abeta.alpha(), x, P),
abeta.beta(), tol);
} // if((P < 0.99) && (Q < 0.99)
} // 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.
// MathCAD test data is to double precision only,
// so set tolerance to 100 eps expressed as a fraction, or
// 100 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.
cout << "Boost::math::tools::epsilon = " << boost::math::tools::epsilon<RealType>() <<endl;
cout << "std::numeric_limits::epsilon = " << std::numeric_limits<RealType>::epsilon() <<endl;
cout << "epsilon = " << tolerance;
tolerance *= 100000; // Note: NO * 100 because is fraction, NOT %.
cout << ", Tolerance = " << tolerance * 100 << "%." << endl;
// RealType teneps = boost::math::tools::epsilon<RealType>() * 10;
// Sources of spot test values:
// MathCAD defines dbeta(x, s1, s2) pdf, s1 == alpha, s2 = beta, x = x in Wolfram
// pbeta(x, s1, s2) cdf and qbeta(x, s1, s2) inverse of cdf
// returns pr(X ,= x) when random variable X
// has the beta distribution with parameters s1)alpha) and s2(beta).
// s1 > 0 and s2 >0 and 0 < x < 1 (but allows x == 0! and x == 1!)
// dbeta(0,1,1) = 0
// dbeta(0.5,1,1) = 1
using boost::math::beta_distribution;
using ::boost::math::cdf;
using ::boost::math::pdf;
// Tests that should throw:
BOOST_MATH_CHECK_THROW(mode(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
// mode is undefined, and throws domain_error!
// BOOST_MATH_CHECK_THROW(median(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
// median is undefined, and throws domain_error!
// But now median IS provided via derived accessor as quantile(half).
BOOST_MATH_CHECK_THROW( // For various bad arguments.
pdf(
beta_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(1)), // bad alpha < 0.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
beta_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad alpha == 0.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad beta == 0.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad beta < 0.
static_cast<RealType>(1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x < 0.
static_cast<RealType>(-1)), std::domain_error);
BOOST_MATH_CHECK_THROW(
pdf(
beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x > 1.
static_cast<RealType>(999)), std::domain_error);
// Some exact pdf values.
BOOST_CHECK_EQUAL( // a = b = 1 is uniform distribution.
pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
static_cast<RealType>(1)), // x
static_cast<RealType>(1));
BOOST_CHECK_EQUAL(
pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
static_cast<RealType>(0)), // x
static_cast<RealType>(1));
BOOST_CHECK_CLOSE_FRACTION(
pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(1),
tolerance);
BOOST_CHECK_EQUAL(
beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)).alpha(),
static_cast<RealType>(1) ); //
BOOST_CHECK_EQUAL(
mean(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))),
static_cast<RealType>(0.5) ); // Exact one half.
BOOST_CHECK_CLOSE_FRACTION(
pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(1.5), // Exactly 3/2
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.5)), // x
static_cast<RealType>(1.5), // Exactly 3/2
tolerance);
// CDF
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.1)), // x
static_cast<RealType>(0.02800000000000000000000000000000000000000L), // Seems exact.
// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=2&b=2&digits=40
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.0001)), // x
static_cast<RealType>(2.999800000000000000000000000000000000000e-8L),
// http://members.aol.com/iandjmsmith/BETAEX.HTM 2.9998000000004
// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.0001&a=2&b=2&digits=40
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.0001)), // x
static_cast<RealType>(0.0005999400000000004L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
// Slightly higher tolerance for real concept:
(std::numeric_limits<RealType>::is_specialized ? 1 : 10) * tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.9999)), // x
static_cast<RealType>(0.999999970002L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
// Wolfram 0.9999999700020000000000000000000000000000
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(2)),
static_cast<RealType>(0.9)), // x
static_cast<RealType>(0.9961174629530394895796514664963063381217L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.1)), // x
static_cast<RealType>(0.2048327646991334516491978475505189480977L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.9)), // x
static_cast<RealType>(0.7951672353008665483508021524494810519023L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.7951672353008665483508021524494810519023L)), // x
static_cast<RealType>(0.9),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.6)), // x
static_cast<RealType>(0.5640942168489749316118742861695149357858L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.5640942168489749316118742861695149357858L)), // x
static_cast<RealType>(0.6),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
static_cast<RealType>(0.6)), // x
static_cast<RealType>(0.1778078083562213736802876784474931812329L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
static_cast<RealType>(0.1778078083562213736802876784474931812329L)), // x
static_cast<RealType>(0.6),
// Wolfram
tolerance); // gives
BOOST_CHECK_CLOSE_FRACTION(
cdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
static_cast<RealType>(0.1)), // x
static_cast<RealType>(0.1), // 0.1000000000000000000000000000000000000000
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
quantile(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
static_cast<RealType>(0.1)), // x
static_cast<RealType>(0.1), // 0.1000000000000000000000000000000000000000
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(complement(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
static_cast<RealType>(0.1))), // complement of x
static_cast<RealType>(0.7951672353008665483508021524494810519023L),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.0280000000000000000000000000000000000L)), // x
static_cast<RealType>(0.1),
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
cdf(complement(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.1))), // x
static_cast<RealType>(0.9720000000000000000000000000000000000000L), // Exact.
// Wolfram
tolerance);
BOOST_CHECK_CLOSE_FRACTION(
pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
static_cast<RealType>(0.9999)), // x
static_cast<RealType>(0.0005999399999999344L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
tolerance*10); // Note loss of precision calculating 1-p test value.
//void test_spot(
// RealType a, // alpha a
// RealType b, // beta b
// RealType x, // Probability
// RealType P, // CDF of beta(a, b)
// RealType Q, // Complement of CDF
// RealType tol) // Test tolerance.
// These test quantiles and complements, and parameter estimates as well.
// Spot values using, for example:
// http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=0.5&b=3&digits=40
test_spot(
static_cast<RealType>(1), // alpha a
static_cast<RealType>(1), // beta b
static_cast<RealType>(0.1), // Probability p
static_cast<RealType>(0.1), // Probability of result (CDF of beta), P
static_cast<RealType>(0.9), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.1), // Probability p
static_cast<RealType>(0.0280000000000000000000000000000000000L), // Probability of result (CDF of beta), P
static_cast<RealType>(1 - 0.0280000000000000000000000000000000000L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.5), // Probability p
static_cast<RealType>(0.5), // Probability of result (CDF of beta), P
static_cast<RealType>(0.5), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.9), // Probability p
static_cast<RealType>(0.972000000000000), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.972000000000000), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.01), // Probability p
static_cast<RealType>(0.0002980000000000000000000000000000000000000L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.0002980000000000000000000000000000000000000L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.001), // Probability p
static_cast<RealType>(2.998000000000000000000000000000000000000E-6L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-2.998000000000000000000000000000000000000E-6L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.0001), // Probability p
static_cast<RealType>(2.999800000000000000000000000000000000000E-8L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-2.999800000000000000000000000000000000000E-8L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(2), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.99), // Probability p
static_cast<RealType>(0.9997020000000000000000000000000000000000L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.9997020000000000000000000000000000000000L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(0.5), // alpha a
static_cast<RealType>(2), // beta b
static_cast<RealType>(0.5), // Probability p
static_cast<RealType>(0.8838834764831844055010554526310612991060L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.8838834764831844055010554526310612991060L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(0.5), // alpha a
static_cast<RealType>(3.), // beta b
static_cast<RealType>(0.7), // Probability p
static_cast<RealType>(0.9903963064097119299191611355232156905687L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.9903963064097119299191611355232156905687L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
test_spot(
static_cast<RealType>(0.5), // alpha a
static_cast<RealType>(3.), // beta b
static_cast<RealType>(0.1), // Probability p
static_cast<RealType>(0.5545844446520295253493059553548880128511L), // Probability of result (CDF of beta), P
static_cast<RealType>(1-0.5545844446520295253493059553548880128511L), // Complement of CDF Q = 1 - P
tolerance); // Test tolerance.
//
// Error checks:
// Construction with 'bad' parameters.
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, -1), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(-1, 1), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, 0), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(0, 1), std::domain_error);
beta_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);
// 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 should throw.
RealType nan = std::numeric_limits<RealType>::quiet_NaN();
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(nan), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, nan), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(nan), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, nan), std::domain_error);
#endif
// Non-finite parameters should throw.
beta_distribution<RealType> w(RealType(1));
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(beta_distribution<RealType> w(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, inf), std::domain_error);
#endif
// Non-finite parameters should throw.
beta_distribution<RealType> w(RealType(1));
#ifndef BOOST_NO_EXCEPTIONS
BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
#else
BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(inf), std::domain_error);
BOOST_MATH_CHECK_THROW(beta_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::beta_distribution<RealType> >(1, 1); // (All) valid constructor parameter values.
// and range and non-finite.
// Not needed??????
BOOST_MATH_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(0, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(-1, 1), 0), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), -1), std::domain_error);
BOOST_MATH_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), 2), std::domain_error);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
BOOST_MATH_CONTROL_FP;
// Check that can generate beta distribution using one convenience methods:
beta_distribution<> mybeta11(1., 1.); // Using default RealType double.
// but that
// boost::math::beta mybeta1(1., 1.); // Using typedef fails.
// error C2039: 'beta' : is not a member of 'boost::math'
// Basic sanity-check spot values.
// Some simple checks using double only.
BOOST_CHECK_EQUAL(mybeta11.alpha(), 1); //
BOOST_CHECK_EQUAL(mybeta11.beta(), 1);
BOOST_CHECK_EQUAL(mean(mybeta11), 0.5); // 1 / (1 + 1) = 1/2 exactly
BOOST_MATH_CHECK_THROW(mode(mybeta11), std::domain_error);
beta_distribution<> mybeta22(2., 2.); // pdf is dome shape.
BOOST_CHECK_EQUAL(mode(mybeta22), 0.5); // 2-1 / (2+2-2) = 1/2 exactly.
beta_distribution<> mybetaH2(0.5, 2.); //
beta_distribution<> mybetaH3(0.5, 3.); //
// Check a few values using double.
BOOST_CHECK_EQUAL(pdf(mybeta11, 1), 1); // is uniform unity over 0 to 1,
BOOST_CHECK_EQUAL(pdf(mybeta11, 0), 1); // including zero and unity.
// Although these next three have an exact result, internally they're
// *not* treated as special cases, and may be out by a couple of eps:
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.5), 1.0, 5*std::numeric_limits<double>::epsilon());
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.0001), 1.0, 5*std::numeric_limits<double>::epsilon());
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.9999), 1.0, 5*std::numeric_limits<double>::epsilon());
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.1), 0.1, 2 * std::numeric_limits<double>::epsilon());
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.5), 0.5, 2 * std::numeric_limits<double>::epsilon());
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.9), 0.9, 2 * std::numeric_limits<double>::epsilon());
BOOST_CHECK_EQUAL(cdf(mybeta11, 1), 1.); // Exact unity expected.
double tol = std::numeric_limits<double>::epsilon() * 10;
BOOST_CHECK_EQUAL(pdf(mybeta22, 1), 0); // is dome shape.
BOOST_CHECK_EQUAL(pdf(mybeta22, 0), 0);
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.5), 1.5, tol); // top of dome, expect exactly 3/2.
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.0001), 5.9994000000000E-4, tol);
BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.9999), 5.9994000000000E-4, tol*50);
BOOST_CHECK_EQUAL(cdf(mybeta22, 0.), 0); // cdf is a curved line from 0 to 1.
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.028000000000000, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.5), 0.5, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.9), 0.972000000000000, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.0001), 2.999800000000000000000000000000000000000E-8, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.001), 2.998000000000000000000000000000000000000E-6, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.01), 0.0002980000000000000000000000000000000000000, tol);
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.02800000000000000000000000000000000000000, tol); // exact
BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.99), 0.9997020000000000000000000000000000000000, tol);
BOOST_CHECK_EQUAL(cdf(mybeta22, 1), 1.); // Exact unity expected.
// Complement
BOOST_CHECK_CLOSE_FRACTION(cdf(complement(mybeta22, 0.9)), 0.028000000000000, tol);
// quantile.
BOOST_CHECK_CLOSE_FRACTION(quantile(mybeta22, 0.028), 0.1, tol);
BOOST_CHECK_CLOSE_FRACTION(quantile(complement(mybeta22, 1 - 0.028)), 0.1, tol);
BOOST_CHECK_EQUAL(kurtosis(mybeta11), 3+ kurtosis_excess(mybeta11)); // Check kurtosis_excess = kurtosis - 3;
BOOST_CHECK_CLOSE_FRACTION(variance(mybeta22), 0.05, tol);
BOOST_CHECK_CLOSE_FRACTION(mean(mybeta22), 0.5, tol);
BOOST_CHECK_CLOSE_FRACTION(mode(mybeta22), 0.5, tol);
BOOST_CHECK_CLOSE_FRACTION(median(mybeta22), 0.5, sqrt(tol)); // Theoretical maximum accuracy using Brent is sqrt(epsilon).
BOOST_CHECK_CLOSE_FRACTION(skewness(mybeta22), 0.0, tol);
BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(mybeta22), -144.0 / 168, tol);
BOOST_CHECK_CLOSE_FRACTION(skewness(beta_distribution<>(3, 5)), 0.30983866769659335081434123198259, tol);
BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_alpha(mean(mybeta22), variance(mybeta22)), mybeta22.alpha(), tol); // mean, variance, probability.
BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_beta(mean(mybeta22), variance(mybeta22)), mybeta22.beta(), tol);// mean, variance, probability.
BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_alpha(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_beta(mybeta22.alpha(), 0.8, cdf(mybeta22, 0.8)), mybeta22.beta(), tol);
beta_distribution<real_concept> rcbeta22(2, 2); // Using RealType real_concept.
cout << "numeric_limits<real_concept>::is_specialized " << numeric_limits<real_concept>::is_specialized << endl;
cout << "numeric_limits<real_concept>::digits " << numeric_limits<real_concept>::digits << endl;
cout << "numeric_limits<real_concept>::digits10 " << numeric_limits<real_concept>::digits10 << endl;
cout << "numeric_limits<real_concept>::epsilon " << numeric_limits<real_concept>::epsilon() << endl;
// (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 )
/*
Output is:
-Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_beta_dist.exe"
Running 1 test case...
numeric_limits<real_concept>::is_specialized 0
numeric_limits<real_concept>::digits 0
numeric_limits<real_concept>::digits10 0
numeric_limits<real_concept>::epsilon 0
Boost::math::tools::epsilon = 1.19209e-007
std::numeric_limits::epsilon = 1.19209e-007
epsilon = 1.19209e-007, Tolerance = 0.0119209%.
Boost::math::tools::epsilon = 2.22045e-016
std::numeric_limits::epsilon = 2.22045e-016
epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
Boost::math::tools::epsilon = 2.22045e-016
std::numeric_limits::epsilon = 2.22045e-016
epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
Boost::math::tools::epsilon = 2.22045e-016
std::numeric_limits::epsilon = 0
epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
*** No errors detected
*/