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Diffstat (limited to 'boost/math/distributions/arcsine.hpp')
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diff --git a/boost/math/distributions/arcsine.hpp b/boost/math/distributions/arcsine.hpp new file mode 100644 index 0000000000..8aad5b2d0b --- /dev/null +++ b/boost/math/distributions/arcsine.hpp @@ -0,0 +1,535 @@ +// boost/math/distributions/arcsine.hpp + +// 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) + +// http://en.wikipedia.org/wiki/arcsine_distribution + +// The arcsine Distribution is a continuous probability distribution. +// http://en.wikipedia.org/wiki/Arcsine_distribution +// http://www.wolframalpha.com/input/?i=ArcSinDistribution + +// Standard arcsine distribution is a special case of beta distribution with both a & b = one half, +// and 0 <= x <= 1. + +// It is generalized to include any bounded support a <= x <= b from 0 <= x <= 1 +// by Wolfram and Wikipedia, +// but using location and scale parameters by +// Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/index.html +// http://www.math.uah.edu/stat/special/Arcsine.html +// The end-point version is simpler and more obvious, so we implement that. +// TODO Perhaps provide location and scale functions? + + +#ifndef BOOST_MATH_DIST_ARCSINE_HPP +#define BOOST_MATH_DIST_ARCSINE_HPP + +#include <boost/math/distributions/fwd.hpp> +#include <boost/math/distributions/complement.hpp> // complements. +#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks. +#include <boost/math/constants/constants.hpp> + +#include <boost/math/special_functions/fpclassify.hpp> // isnan. + +#if defined (BOOST_MSVC) +# pragma warning(push) +# pragma warning(disable: 4702) // Unreachable code, +// in domain_error_imp in error_handling. +#endif + +#include <utility> +#include <exception> // For std::domain_error. + +namespace boost +{ + namespace math + { + namespace arcsine_detail + { + // Common error checking routines for arcsine distribution functions: + // Duplicating for x_min and x_max provides specific error messages. + template <class RealType, class Policy> + inline bool check_x_min(const char* function, const RealType& x, RealType* result, const Policy& pol) + { + if (!(boost::math::isfinite)(x)) + { + *result = policies::raise_domain_error<RealType>( + function, + "x_min argument is %1%, but must be finite !", x, pol); + return false; + } + return true; + } // bool check_x_min + + template <class RealType, class Policy> + inline bool check_x_max(const char* function, const RealType& x, RealType* result, const Policy& pol) + { + if (!(boost::math::isfinite)(x)) + { + *result = policies::raise_domain_error<RealType>( + function, + "x_max argument is %1%, but must be finite !", x, pol); + return false; + } + return true; + } // bool check_x_max + + + template <class RealType, class Policy> + inline bool check_x_minmax(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol) + { // Check x_min < x_max + if (x_min >= x_max) + { + std::string msg = "x_max argument is %1%, but must be > x_min = " + lexical_cast<std::string>(x_min) + "!"; + *result = policies::raise_domain_error<RealType>( + function, + msg.c_str(), x_max, pol); + // "x_max argument is %1%, but must be > x_min !", x_max, pol); + // "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. + // But would require replication of all helpers functions in /policies/error_handling.hpp for two values, + // as well as two value versions of raise_error, raise_domain_error and do_format ... + // so use slightly hacky lexical_cast to string instead. + return false; + } + return true; + } // bool check_x_minmax + + template <class RealType, class Policy> + inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol) + { + if ((p < 0) || (p > 1) || !(boost::math::isfinite)(p)) + { + *result = policies::raise_domain_error<RealType>( + function, + "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol); + return false; + } + return true; + } // bool check_prob + + template <class RealType, class Policy> + inline bool check_x(const char* function, const RealType& x_min, const RealType& x_max, const RealType& x, RealType* result, const Policy& pol) + { // Check x finite and x_min < x < x_max. + if (!(boost::math::isfinite)(x)) + { + *result = policies::raise_domain_error<RealType>( + function, + "x argument is %1%, but must be finite !", x, pol); + return false; + } + if ((x < x_min) || (x > x_max)) + { + // std::cout << x_min << ' ' << x << x_max << std::endl; + *result = policies::raise_domain_error<RealType>( + function, + "x argument is %1%, but must be x_min < x < x_max !", x, pol); + // For example: + // Error in function boost::math::pdf(arcsine_distribution<double> const&, double) : x argument is -1.01, but must be x_min < x < x_max ! + // TODO Perhaps show values of x_min and x_max? + return false; + } + return true; + } // bool check_x + + template <class RealType, class Policy> + inline bool check_dist(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol) + { // Check both x_min and x_max finite, and x_min < x_max. + return check_x_min(function, x_min, result, pol) + && check_x_max(function, x_max, result, pol) + && check_x_minmax(function, x_min, x_max, result, pol); + } // bool check_dist + + template <class RealType, class Policy> + inline bool check_dist_and_x(const char* function, const RealType& x_min, const RealType& x_max, RealType x, RealType* result, const Policy& pol) + { + return check_dist(function, x_min, x_max, result, pol) + && arcsine_detail::check_x(function, x_min, x_max, x, result, pol); + } // bool check_dist_and_x + + template <class RealType, class Policy> + inline bool check_dist_and_prob(const char* function, const RealType& x_min, const RealType& x_max, RealType p, RealType* result, const Policy& pol) + { + return check_dist(function, x_min, x_max, result, pol) + && check_prob(function, p, result, pol); + } // bool check_dist_and_prob + + } // namespace arcsine_detail + + template <class RealType = double, class Policy = policies::policy<> > + class arcsine_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + arcsine_distribution(RealType x_min = 0, RealType x_max = 1) : m_x_min(x_min), m_x_max(x_max) + { // Default beta (alpha = beta = 0.5) is standard arcsine with x_min = 0, x_max = 1. + // Generalized to allow x_min and x_max to be specified. + RealType result; + arcsine_detail::check_dist( + "boost::math::arcsine_distribution<%1%>::arcsine_distribution", + m_x_min, + m_x_max, + &result, Policy()); + } // arcsine_distribution constructor. + // Accessor functions: + RealType x_min() const + { + return m_x_min; + } + RealType x_max() const + { + return m_x_max; + } + + private: + RealType m_x_min; // Two x min and x max parameters of the arcsine distribution. + RealType m_x_max; + }; // template <class RealType, class Policy> class arcsine_distribution + + // Convenient typedef to construct double version. + typedef arcsine_distribution<double> arcsine; + + + template <class RealType, class Policy> + inline const std::pair<RealType, RealType> range(const arcsine_distribution<RealType, Policy>& dist) + { // Range of permissible values for random variable x. + using boost::math::tools::max_value; + return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max())); + } + + template <class RealType, class Policy> + inline const std::pair<RealType, RealType> support(const arcsine_distribution<RealType, Policy>& dist) + { // Range of supported values for random variable x. + // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. + return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max())); + } + + template <class RealType, class Policy> + inline RealType mean(const arcsine_distribution<RealType, Policy>& dist) + { // Mean of arcsine distribution . + RealType result; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + if (false == arcsine_detail::check_dist( + "boost::math::mean(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + return (x_min + x_max) / 2; + } // mean + + template <class RealType, class Policy> + inline RealType variance(const arcsine_distribution<RealType, Policy>& dist) + { // Variance of standard arcsine distribution = (1-0)/8 = 0.125. + RealType result; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + if (false == arcsine_detail::check_dist( + "boost::math::variance(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + return (x_max - x_min) * (x_max - x_min) / 8; + } // variance + + template <class RealType, class Policy> + inline RealType mode(const arcsine_distribution<RealType, Policy>& /* dist */) + { //There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1, + // so instead we raise the exception domain_error. + return policies::raise_domain_error<RealType>( + "boost::math::mode(arcsine_distribution<%1%>&)", + "The arcsine distribution has two modes at x_min and x_max: " + "so the return value is %1%.", + std::numeric_limits<RealType>::quiet_NaN(), Policy()); + } // mode + + template <class RealType, class Policy> + inline RealType median(const arcsine_distribution<RealType, Policy>& dist) + { // Median of arcsine distribution (a + b) / 2 == mean. + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + RealType result; + if (false == arcsine_detail::check_dist( + "boost::math::median(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + return (x_min + x_max) / 2; + } + + template <class RealType, class Policy> + inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist) + { + RealType result; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + if (false == arcsine_detail::check_dist( + "boost::math::skewness(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + return 0; + } // skewness + + template <class RealType, class Policy> + inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist) + { + RealType result; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + if (false == arcsine_detail::check_dist( + "boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + result = -3; + return result / 2; + } // kurtosis_excess + + template <class RealType, class Policy> + inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist) + { + RealType result; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + if (false == arcsine_detail::check_dist( + "boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )", + x_min, + x_max, + &result, Policy()) + ) + { + return result; + } + + return 3 + kurtosis_excess(dist); + } // kurtosis + + template <class RealType, class Policy> + inline RealType pdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& xx) + { // Probability Density/Mass Function arcsine. + BOOST_FPU_EXCEPTION_GUARD + BOOST_MATH_STD_USING // For ADL of std functions. + + static const char* function = "boost::math::pdf(arcsine_distribution<%1%> const&, %1%)"; + + RealType lo = dist.x_min(); + RealType hi = dist.x_max(); + RealType x = xx; + + // Argument checks: + RealType result = 0; + if (false == arcsine_detail::check_dist_and_x( + function, + lo, hi, x, + &result, Policy())) + { + return result; + } + using boost::math::constants::pi; + result = static_cast<RealType>(1) / (pi<RealType>() * sqrt((x - lo) * (hi - x))); + return result; + } // pdf + + template <class RealType, class Policy> + inline RealType cdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& x) + { // Cumulative Distribution Function arcsine. + BOOST_MATH_STD_USING // For ADL of std functions. + + static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)"; + + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + // Argument checks: + RealType result = 0; + if (false == arcsine_detail::check_dist_and_x( + function, + x_min, x_max, x, + &result, Policy())) + { + return result; + } + // Special cases: + if (x == x_min) + { + return 0; + } + else if (x == x_max) + { + return 1; + } + using boost::math::constants::pi; + result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); + return result; + } // arcsine cdf + + template <class RealType, class Policy> + inline RealType cdf(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c) + { // Complemented Cumulative Distribution Function arcsine. + BOOST_MATH_STD_USING // For ADL of std functions. + static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)"; + + RealType x = c.param; + arcsine_distribution<RealType, Policy> const& dist = c.dist; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + + // Argument checks: + RealType result = 0; + if (false == arcsine_detail::check_dist_and_x( + function, + x_min, x_max, x, + &result, Policy())) + { + return result; + } + if (x == x_min) + { + return 0; + } + else if (x == x_max) + { + return 1; + } + using boost::math::constants::pi; + // Naive version x = 1 - x; + // result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); + // is less accurate, so use acos instead of asin for complement. + result = static_cast<RealType>(2) * acos(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); + return result; + } // arcine ccdf + + template <class RealType, class Policy> + inline RealType quantile(const arcsine_distribution<RealType, Policy>& dist, const RealType& p) + { + // Quantile or Percent Point arcsine function or + // Inverse Cumulative probability distribution function CDF. + // Return x (0 <= x <= 1), + // for a given probability p (0 <= p <= 1). + // These functions take a probability as an argument + // and return a value such that the probability that a random variable x + // will be less than or equal to that value + // is whatever probability you supplied as an argument. + BOOST_MATH_STD_USING // For ADL of std functions. + + using boost::math::constants::half_pi; + + static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)"; + + RealType result = 0; // of argument checks: + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + if (false == arcsine_detail::check_dist_and_prob( + function, + x_min, x_max, p, + &result, Policy())) + { + return result; + } + // Special cases: + if (p == 0) + { + return 0; + } + if (p == 1) + { + return 1; + } + + RealType sin2hpip = sin(half_pi<RealType>() * p); + RealType sin2hpip2 = sin2hpip * sin2hpip; + result = -x_min * sin2hpip2 + x_min + x_max * sin2hpip2; + + return result; + } // quantile + + template <class RealType, class Policy> + inline RealType quantile(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c) + { + // Complement Quantile or Percent Point arcsine function. + // Return the number of expected x for a given + // complement of the probability q. + BOOST_MATH_STD_USING // For ADL of std functions. + + using boost::math::constants::half_pi; + static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)"; + + // Error checks: + RealType q = c.param; + const arcsine_distribution<RealType, Policy>& dist = c.dist; + RealType result = 0; + RealType x_min = dist.x_min(); + RealType x_max = dist.x_max(); + if (false == arcsine_detail::check_dist_and_prob( + function, + x_min, + x_max, + q, + &result, Policy())) + { + return result; + } + // Special cases: + if (q == 1) + { + return 0; + } + if (q == 0) + { + return 1; + } + // Naive RealType p = 1 - q; result = sin(half_pi<RealType>() * p); loses accuracy, so use a cos alternative instead. + //result = cos(half_pi<RealType>() * q); // for arcsine(0,1) + //result = result * result; + // For generalized arcsine: + RealType cos2hpip = cos(half_pi<RealType>() * q); + RealType cos2hpip2 = cos2hpip * cos2hpip; + result = -x_min * cos2hpip2 + x_min + x_max * cos2hpip2; + + return result; + } // Quantile Complement + + } // namespace math +} // namespace boost + +// This include must be at the end, *after* the accessors +// for this distribution have been defined, in order to +// keep compilers that support two-phase lookup happy. +#include <boost/math/distributions/detail/derived_accessors.hpp> + +#if defined (BOOST_MSVC) +# pragma warning(pop) +#endif + +#endif // BOOST_MATH_DIST_ARCSINE_HPP |