| // test_beta_dist.cpp |
| |
| // Copyright John Maddock 2006. |
| // Copyright Paul A. Bristow 2007, 2009. |
| |
| // 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 |
| # pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored |
| #endif |
| |
| #include <boost/math/concepts/real_concept.hpp> // for real_concept |
| using ::boost::math::concepts::real_concept; |
| |
| #include <boost/math/distributions/beta.hpp> // for beta_distribution |
| using boost::math::beta_distribution; |
| using boost::math::beta; |
| |
| #include <boost/test/test_exec_monitor.hpp> // for test_main |
| #include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION |
| |
| #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_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_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_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_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_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_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_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_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. |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| 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_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, tol); |
| |
| 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 |
| return 0; |
| } // int test_main(int, char* []) |
| |
| /* |
| |
| 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 |
| */ |
| |
| |
| |
