diff --git a/include/boost/math/distributions/geometric.hpp b/include/boost/math/distributions/geometric.hpp new file mode 100644 index 000000000..4aa51746f --- /dev/null +++ b/include/boost/math/distributions/geometric.hpp @@ -0,0 +1,516 @@ +// boost\math\distributions\geometric.hpp + +// Copyright John Maddock 2010. +// Copyright Paul A. Bristow 2010. + +// 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) + +// geometric distribution is a discrete probability distribution. +// It expresses the probability distribution of the number (k) of +// events, occurrences, failures or arrivals before the first success. +// supported on the set {0, 1, 2, 3...} + +// Note that the set includes zero (unlike some definitions that start at one). + +// The random variate k is the number of events, occurrences or arrivals. +// k argument may be integral, signed, or unsigned, or floating point. +// If necessary, it has already been promoted from an integral type. + +// Note that the geometric distribution +// (like others including the binomial, geometric & Bernoulli) +// is strictly defined as a discrete function: +// only integral values of k are envisaged. +// However because the method of calculation uses a continuous gamma function, +// it is convenient to treat it as if a continous function, +// and permit non-integral values of k. +// To enforce the strict mathematical model, users should use floor or ceil functions +// on k outside this function to ensure that k is integral. + +// See http://en.wikipedia.org/wiki/geometric_distribution +// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html +// http://mathworld.wolfram.com/GeometricDistribution.html + +#ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP +#define BOOST_MATH_SPECIAL_GEOMETRIC_HPP + +#include +#include // for ibeta(a, b, x) == Ix(a, b). +#include // complement. +#include // error checks domain_error & logic_error. +#include // isnan. +#include // for root finding. +#include + +#include +#include +#include +#include + +#include // using std::numeric_limits; +#include + +#if defined (BOOST_MSVC) +# pragma warning(push) +// This believed not now necessary, so commented out. +//# pragma warning(disable: 4702) // unreachable code. +// in domain_error_imp in error_handling. +#endif + +namespace boost +{ + namespace math + { + namespace geometric_detail + { + // Common error checking routines for geometric distribution function: + template + inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) + { + if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) ) + { + *result = policies::raise_domain_error( + function, + "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); + return false; + } + return true; + } + + template + inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol) + { + return check_success_fraction(function, p, result, pol); + } + + template + inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol) + { + if(check_dist(function, p, result, pol) == false) + { + return false; + } + if( !(boost::math::isfinite)(k) || (k < 0) ) + { // Check k failures. + *result = policies::raise_domain_error( + function, + "Number of failures argument is %1%, but must be >= 0 !", k, pol); + return false; + } + return true; + } // Check_dist_and_k + + template + inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol) + { + if(check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol) == false) + { + return false; + } + return true; + } // check_dist_and_prob + } // namespace geometric_detail + + template > + class geometric_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + geometric_distribution(RealType p) : m_p(p) + { // Constructor stores success_fraction p. + RealType result; + geometric_detail::check_dist( + "geometric_distribution<%1%>::geometric_distribution", + m_p, // Check success_fraction 0 <= p <= 1. + &result, Policy()); + } // geometric_distribution constructor. + + // Private data getter class member functions. + RealType success_fraction() const + { // Probability of success as fraction in range 0 to 1. + return m_p; + } + RealType successes() const + { // Total number of successes r = 1 (for compatibility with negative binomial?). + return 1; + } + + // Parameter estimation. + // (These are copies of negative_binomial distribution with successes = 1). + static RealType find_lower_bound_on_p( + RealType trials, + RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. + { + static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p"; + RealType result; // of error checks. + RealType successes = 1; + RealType failures = trials - successes; + if(false == detail::check_probability(function, alpha, &result, Policy()) + && geometric_detail::check_dist_and_k( + function, RealType(0), failures, &result, Policy())) + { + return result; + } + // Use complement ibeta_inv function for lower bound. + // This is adapted from the corresponding binomial formula + // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm + // This is a Clopper-Pearson interval, and may be overly conservative, + // see also "A Simple Improved Inferential Method for Some + // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY + // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf + // + return ibeta_inv(successes, failures + 1, alpha, static_cast(0), Policy()); + } // find_lower_bound_on_p + + static RealType find_upper_bound_on_p( + RealType trials, + RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. + { + static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p"; + RealType result; // of error checks. + RealType successes = 1; + RealType failures = trials - successes; + if(false == geometric_detail::check_dist_and_k( + function, RealType(0), failures, &result, Policy()) + && detail::check_probability(function, alpha, &result, Policy())) + { + return result; + } + if(failures == 0) + { + return 1; + }// Use complement ibetac_inv function for upper bound. + // Note adjusted failures value: *not* failures+1 as usual. + // This is adapted from the corresponding binomial formula + // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm + // This is a Clopper-Pearson interval, and may be overly conservative, + // see also "A Simple Improved Inferential Method for Some + // Discrete Distributions" Yong CAI and K. Krishnamoorthy + // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf + // + return ibetac_inv(successes, failures, alpha, static_cast(0), Policy()); + } // find_upper_bound_on_p + + // Estimate number of trials : + // "How many trials do I need to be P% sure of seeing k or fewer failures?" + + static RealType find_minimum_number_of_trials( + RealType k, // number of failures (k >= 0). + RealType p, // success fraction 0 <= p <= 1. + RealType alpha) // risk level threshold 0 <= alpha <= 1. + { + static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials"; + // Error checks: + RealType result; + if(false == geometric_detail::check_dist_and_k( + function, p, k, &result, Policy()) + && detail::check_probability(function, alpha, &result, Policy())) + { + return result; + } + result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k + return result + k; + } // RealType find_number_of_failures + + static RealType find_maximum_number_of_trials( + RealType k, // number of failures (k >= 0). + RealType p, // success fraction 0 <= p <= 1. + RealType alpha) // risk level threshold 0 <= alpha <= 1. + { + static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials"; + // Error checks: + RealType result; + if(false == geometric_detail::check_dist_and_k( + function, p, k, &result, Policy()) + && detail::check_probability(function, alpha, &result, Policy())) + { + return result; + } + result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k + return result + k; + } // RealType find_number_of_trials complemented + + private: + //RealType m_r; // successes fixed at unity. + RealType m_p; // success_fraction + }; // template class geometric_distribution + + typedef geometric_distribution geometric; // Reserved name of type double. + + template + inline const std::pair range(const geometric_distribution& /* dist */) + { // Range of permissible values for random variable k. + using boost::math::tools::max_value; + return std::pair(static_cast(0), max_value()); // max_integer? + } + + template + inline const std::pair support(const geometric_distribution& /* dist */) + { // Range of supported values for random variable k. + // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. + using boost::math::tools::max_value; + return std::pair(static_cast(0), max_value()); // max_integer? + } + + template + inline RealType mean(const geometric_distribution& dist) + { // Mean of geometric distribution = (1-p)/p. + return (1 - dist.success_fraction() ) / dist.success_fraction(); + } // mean + + // median implemented via quantile(half) in derived accessors. + + template + inline RealType mode(const geometric_distribution&) + { // Mode of geometric distribution = zero. + BOOST_MATH_STD_USING // ADL of std functions. + return 0; + } // mode + + template + inline RealType variance(const geometric_distribution& dist) + { // Variance of Binomial distribution = (1-p) / p^2. + return (1 - dist.success_fraction()) + / (dist.success_fraction() * dist.success_fraction()); + } // variance + + template + inline RealType skewness(const geometric_distribution& dist) + { // skewness of geometric distribution = 2-p / (sqrt(r(1-p)) + BOOST_MATH_STD_USING // ADL of std functions. + RealType p = dist.success_fraction(); + return (2 - p) / sqrt(1 - p); + } // skewness + + template + inline RealType kurtosis(const geometric_distribution& dist) + { // kurtosis of geometric distribution + // http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3 + RealType p = dist.success_fraction(); + return 3 + (p*p - 6*p + 6) / (1 - p); + } // kurtosis + + template + inline RealType kurtosis_excess(const geometric_distribution& dist) + { // kurtosis excess of geometric distribution + // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess + RealType p = dist.success_fraction(); + return (p*p - 6*p + 6) / (1 - p); + } // kurtosis_excess + + // RealType standard_deviation(const geometric_distribution& dist) + // standard_deviation provided by derived accessors. + // RealType hazard(const geometric_distribution& dist) + // hazard of geometric distribution provided by derived accessors. + // RealType chf(const geometric_distribution& dist) + // chf of geometric distribution provided by derived accessors. + + template + inline RealType pdf(const geometric_distribution& dist, const RealType& k) + { // Probability Density/Mass Function. + BOOST_FPU_EXCEPTION_GUARD + BOOST_MATH_STD_USING // For ADL of math functions. + static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)"; + + RealType p = dist.success_fraction(); + RealType result; + if(false == geometric_detail::check_dist_and_k( + function, + p, + k, + &result, Policy())) + { + return result; + } + if (k == 0) + { + return p; // success_fraction + } + RealType q = 1 - p; // Inaccurate for small p? + // So try to avoid inaccuracy for large or small p. + // but has little effect > last significant bit. + //cout << "p * pow(q, k) " << result << endl; // seems best whatever p + //cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl; + //if (p < 0.5) + //{ + // result = p * pow(q, k); + //} + //else + //{ + // result = p * exp(k * log1p(-p)); + //} + result = p * pow(q, k); + return result; + } // geometric_pdf + + template + inline RealType cdf(const geometric_distribution& dist, const RealType& k) + { // Cumulative Distribution Function of geometric. + static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; + + // k argument may be integral, signed, or unsigned, or floating point. + // If necessary, it has already been promoted from an integral type. + RealType p = dist.success_fraction(); + // Error check: + RealType result; + if(false == geometric_detail::check_dist_and_k( + function, + p, + k, + &result, Policy())) + { + return result; + } + if(k == 0) + { + return p; // success_fraction + } + //RealType q = 1 - p; // Bad for small p + //RealType probability = 1 - std::pow(q, k+1); + + RealType z = log1p(-p) * (k+1); + RealType probability = -expm1(z); + + return probability; + } // cdf Cumulative Distribution Function geometric. + + template + inline RealType cdf(const complemented2_type, RealType>& c) + { // Complemented Cumulative Distribution Function geometric. + + static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; + // k argument may be integral, signed, or unsigned, or floating point. + // If necessary, it has already been promoted from an integral type. + RealType const& k = c.param; + geometric_distribution const& dist = c.dist; + RealType p = dist.success_fraction(); + // Error check: + RealType result; + if(false == geometric_detail::check_dist_and_k( + function, + p, + k, + &result, Policy())) + { + return result; + } + RealType z = log1p(-p) * (k+1); + RealType probability = exp(z); + return probability; + } // cdf Complemented Cumulative Distribution Function geometric. + + template + inline RealType quantile(const geometric_distribution& dist, const RealType& x) + { // Quantile, percentile/100 or Percent Point geometric function. + // Return the number of expected failures k for a given probability p. + + // Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability. + // k argument may be integral, signed, or unsigned, or floating point. + + static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; + BOOST_MATH_STD_USING // ADL of std functions. + + RealType success_fraction = dist.success_fraction(); + // Check dist and x. + RealType result; + if(false == geometric_detail::check_dist_and_prob + (function, success_fraction, x, &result, Policy())) + { + return result; + } + + // Special cases. + if (x == 1) + { // Would need +infinity failures for total confidence. + result = policies::raise_overflow_error( + function, + "Probability argument is 1, which implies infinite failures !", Policy()); + return result; + // usually means return +std::numeric_limits::infinity(); + // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR + } + if (x == 0) + { // No failures are expected if P = 0. + return 0; // Total trials will be just dist.successes. + } + // if (P <= pow(dist.success_fraction(), 1)) + if (x <= success_fraction) + { // p <= pdf(dist, 0) == cdf(dist, 0) + return 0; + } + if (x == 1) + { + return 0; + } + + // log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small + result = log1p(-x) / log1p(-success_fraction) -1; + // Subtract a few epsilons here too? + // to make sure it doesn't slip over, so ceil would be one too many. + return result; + } // RealType quantile(const geometric_distribution dist, p) + + template + inline RealType quantile(const complemented2_type, RealType>& c) + { // Quantile or Percent Point Binomial function. + // Return the number of expected failures k for a given + // complement of the probability Q = 1 - P. + static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; + + // Error checks: + RealType x = c.param; + const geometric_distribution& dist = c.dist; + RealType success_fraction = dist.success_fraction(); + RealType result; + if(false == geometric_detail::check_dist_and_prob( + function, + success_fraction, + x, + &result, Policy())) + { + return result; + } + + // Special cases: + if(x == 1) + { // There may actually be no answer to this question, + // since the probability of zero failures may be non-zero, + return 0; // but zero is the best we can do: + } + if (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy())) + { // q <= cdf(complement(dist, 0)) == pdf(dist, 0) + return 0; // + } + if(x == 0) + { // Probability 1 - Q == 1 so infinite failures to achieve certainty. + // Would need +infinity failures for total confidence. + result = policies::raise_overflow_error( + function, + "Probability argument complement is 0, which implies infinite failures !", Policy()); + return result; + // usually means return +std::numeric_limits::infinity(); + // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR + } + // log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small + result = log(x) / log1p(-success_fraction) -1; + 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 + +#if defined (BOOST_MSVC) +# pragma warning(pop) +#endif + +#endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP diff --git a/include/boost/math/distributions/inverse_gaussian.hpp b/include/boost/math/distributions/inverse_gaussian.hpp new file mode 100644 index 000000000..05a60178f --- /dev/null +++ b/include/boost/math/distributions/inverse_gaussian.hpp @@ -0,0 +1,578 @@ +// Copyright John Maddock 2010. +// Copyright Paul A. Bristow 2010. + +// 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) + +#ifndef BOOST_STATS_INVERSE_GAUSSIAN_HPP +#define BOOST_STATS_INVERSE_GAUSSIAN_HPP + +// http://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution +// http://mathworld.wolfram.com/InverseGaussianDistribution.html + +// The normal-inverse Gaussian distribution +// also called the Wald distribution (some sources limit this to when mean = 1). + +// It is the continuous probability distribution +// that is defined as the normal variance-mean mixture where the mixing density is the +// inverse Gaussian distribution. The tails of the distribution decrease more slowly +// than the normal distribution. It is therefore suitable to model phenomena +// where numerically large values are more probable than is the case for the normal distribution. + +// The Inverse Gaussian distribution was first studied in relationship to Brownian motion. +// In 1956 M.C.K. Tweedie used the name 'Inverse Gaussian' because there is an inverse +// relationship between the time to cover a unit distance and distance covered in unit time. + +// Examples are returns from financial assets and turbulent wind speeds. +// The normal-inverse Gaussian distributions form +// a subclass of the generalised hyperbolic distributions. + +// See also + +// http://en.wikipedia.org/wiki/Normal_distribution +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm +// Also: +// Weisstein, Eric W. "Normal Distribution." +// From MathWorld--A Wolfram Web Resource. +// http://mathworld.wolfram.com/NormalDistribution.html + +// http://www.jstatsoft.org/v26/i04/paper General class of inverse Gaussian distributions. +// ig package - withdrawn but at http://cran.r-project.org/src/contrib/Archive/ig/ + +// http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/SuppDists/html/inverse_gaussian.html +// R package for dinverse_gaussian, ... + +// http://www.statsci.org/s/inverse_gaussian.s and http://www.statsci.org/s/inverse_gaussian.html + +//#include +#include // for erf/erfc. +#include +#include +#include +#include // for gamma function +// using boost::math::gamma_p; + +#include +//using std::tr1::tuple; +//using std::tr1::make_tuple; +#include +//using boost::math::tools::newton_raphson_iterate; + +#include + +namespace boost{ namespace math{ + +template > +class inverse_gaussian_distribution +{ +public: + typedef RealType value_type; + typedef Policy policy_type; + + inverse_gaussian_distribution(RealType mean = 1, RealType scale = 1) + : m_mean(mean), m_scale(scale) + { // Default is a 1,1 inverse_gaussian distribution. + static const char* function = "boost::math::inverse_gaussian_distribution<%1%>::inverse_gaussian_distribution"; + + RealType result; + detail::check_scale(function, scale, &result, Policy()); + detail::check_location(function, mean, &result, Policy()); + } + + RealType mean()const + { // alias for location. + return m_mean; // aka mu + } + + // Synonyms, provided to allow generic use of find_location and find_scale. + RealType location()const + { // location, aka mu. + return m_mean; + } + RealType scale()const + { // scale, aka lambda. + return m_scale; + } + + RealType shape()const + { // shape, aka phi = lambda/mu. + return m_scale / m_mean; + } + +private: + // + // Data members: + // + RealType m_mean; // distribution mean or location, aka mu. + RealType m_scale; // distribution standard deviation or scale, aka lambda. +}; // class normal_distribution + +typedef inverse_gaussian_distribution inverse_gaussian; + +template +inline const std::pair range(const inverse_gaussian_distribution& /*dist*/) +{ // Range of permissible values for random variable x, zero to max. + using boost::math::tools::max_value; + return std::pair(static_cast(0.), max_value()); // - to + max value. +} + +template +inline const std::pair support(const inverse_gaussian_distribution& /*dist*/) +{ // Range of supported values for random variable x, zero to max. + // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. + using boost::math::tools::max_value; + return std::pair(static_cast(0.), max_value()); // - to + max value. +} + +template +inline RealType pdf(const inverse_gaussian_distribution& dist, const RealType& x) +{ // Probability Density Function + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result; + static const char* function = "boost::math::pdf(const inverse_gaussian_distribution<%1%>&, %1%)"; + if(false == detail::check_scale(function, scale, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if(false == detail::check_positive_x(function, x, &result, Policy())) + { + return std::numeric_limits::quiet_NaN(); + } + + if (x == 0) + { + return 0; // Convenient, even if not defined mathematically. + } + + result = + sqrt(scale / (constants::two_pi() * x * x * x)) + * exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean)); + return result; +} // pdf + +template +inline RealType cdf(const inverse_gaussian_distribution& dist, const RealType& x) +{ // Cumulative Density Function. + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = dist.scale(); + RealType mean = dist.mean(); + static const char* function = "boost::math::cdf(const inverse_gaussian_distribution<%1%>&, %1%)"; + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if(false == detail::check_positive_x(function, x, &result, Policy())) + { + return result; + } + if (x == 0) + { + return 0; // Convenient, even if not defined mathematically. + } + // Problem with this formula for large scale > 1000 or small x, + //result = 0.5 * (erf(sqrt(scale / x) * ((x / mean) - 1) / constants::root_two(), Policy()) + 1) + // + exp(2 * scale / mean) / 2 + // * (1 - erf(sqrt(scale / x) * (x / mean + 1) / constants::root_two(), Policy())); + // so use normal distribution version: + // Wikipedia CDF equation http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution. + + normal_distribution n01; + + RealType n0 = sqrt(scale / x); + n0 *= ((x / mean) -1); + RealType n1 = cdf(n01, n0); + RealType expfactor = exp(2 * scale / mean); + RealType n3 = - sqrt(scale / x); + n3 *= (x / mean) + 1; + // cout << "((x / mean) +1) = " << n3 << endl; + RealType n4 = cdf(n01, n3); + //cout << "phi1 = " << n1 << ", exp(2 * scale / mean) = " << n2 << ", exp * phi2 = " << n4 * n2 << endl; + + result = n1 + expfactor * n4; + + if(false) + { // Output some diagnostic values. + cout <<"_\n cdf===========================" << endl; + cout << "sqrt(scale / x)*((x / mean) -1) = " << n0 << endl; + cout << "cdf(n01, n1) = " << n1 << endl; + cout << "exp(2 * scale / mean) = " << expfactor << endl; + cout << " - sqrt(scale / x)*((x / mean) +1) = " << n3 << endl; + cout << "cdf(n01, - sqrt(scale / x)*((x / mean) +1)) = " << n4 << endl; + cout << "exp * cdf_2 = " << n4 * expfactor << endl; + cout << "cdf_1 + exp * cdf_2 = " << result << endl; + } + return result; +} // cdf + +template +struct inverse_gaussian_quantile_functor +{ + + inverse_gaussian_quantile_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) + : distribution(dist), prob(p) + { + } + boost::math::tuple operator()(RealType const& x) + { + RealType c = cdf(distribution, x); + RealType fx = c - prob; // Difference cdf - value - to minimize. + RealType dx = pdf(distribution, x); // pdf is 1st derivative. + if(false) + { + cout << "cdf(dist, " << x << ") = " << c << ", diff = " << fx << ", dx " << dx << endl; + } + // return both function evaluation difference f(x) and 1st derivative f'(x). + return std::tr1::make_tuple(fx, dx); + } + private: + const boost::math::inverse_gaussian_distribution distribution; + RealType prob; +}; + +template +struct inverse_gaussian_quantile_complement_functor +{ + inverse_gaussian_quantile_complement_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) + : distribution(dist), prob(p) + { + } + boost::math::tuple operator()(RealType const& x) + { + RealType c = cdf(complement(distribution, x)); + RealType fx = c - prob; // Difference cdf - value - to minimize. + RealType dx = -pdf(distribution, x); // pdf is 1st derivative. + if(true) + { + std::streamsize precision = cout.precision(); // Save + if (false) + { + cout << setprecision(numeric_limits::max_digits10) + << "cdf((complement(dist, " << x << ")) = " << c + << setprecision(4) + << ", diff = " << fx << ", dx " << dx << endl; + cout.precision(precision); // restore + } + } + // return both function evaluation difference f(x) and 1st derivative f'(x). + return std::tr1::make_tuple(fx, dx); + } + private: + const boost::math::inverse_gaussian_distribution distribution; + RealType prob; +}; + +namespace detail +{ + template + inline RealType guess_ig(RealType p, RealType mu = 1, RealType lambda = 1) + { // guess at random variate value x for inverse gaussian quantile. + using boost::math::policies::policy; + // Error type. + using boost::math::policies::overflow_error; + // Action. + using boost::math::policies::ignore_error; + + typedef policy< + overflow_error // Ignore overflow (return infinity) + > no_overthrow_policy; + + RealType x; // result is guess at random variate value x. + RealType phi = lambda / mu; + if (phi > 2.) + { // Big phi, so starting to look like normal Gaussian distribution. + // x=(qnorm(p,0,1,true,false) - 0.5 * sqrt(mu/lambda)) / sqrt(lambda/mu); + // Whitmore, G.A. and Yalovsky, M. + // A normalising logarithmic transformation for inverse Gaussian random variables, + // Technometrics 20-2, 207-208 (1978), but using expression from + // V Seshadri, Inverse Gaussian distribution (1998) ISBN 0387 98618 9, page 6. + //x = qnorm(p, 0, 1, true, false); + //x /= sqrt(phi); + //x = x - 1. / (2 * phi); + //x = mu * exp(x); + // x = mu * exp(qnorm(p, 0, 1, true, false) / sqrt(phi) - 1/(2 * phi)); + normal_distribution n01; + x = mu * exp(quantile(n01, p) / sqrt(phi) - 1/(2 * phi)); + // Might add about 0.006 to this to get closer? + //RealType pi = 3.1459; + //cout << "1 / sqrt(8 * pi * phi) = " << 1 / sqrt(8 * pi * phi) << endl; + // Bagshaw guess is: + // RealType U = quantile(n01, p); // U <- qnorm (p) + // RealType r1 = 1 + U / sqrt (phi) + U * U / (2 * phi) + U * U * U / (8 * phi * sqrt(phi)); + } + else + { // phi < 2 so much less symmetrical with long tail, + // so use gamma distribution as an approximation. + using boost::math::gamma_distribution; + + // Define the distribution, using gamma_nooverflow: + typedef gamma_distribution gamma_nooverflow; + + gamma_distribution g(static_cast(0.5), static_cast(1.)); + + // gamma_nooverflow g(static_cast(0.5), static_cast(1.)); + // R qgamma(0.2, 0.5, 1) 0.0320923 + RealType qg = quantile(complement(g, p)); + //RealType qg1 = qgamma(1.- p, 0.5, 1.0, true, false); + //cout << "quantile(complement(g, p)) = " << qg << ", qgamma(1.- p, 0.5, 1.0, true, false); = " << qg1 << endl; // 49.014664823030209 1.#INF + x = lambda / (qg * 2); + // + if (x > mu/2) // x > mu /2? + { // x too large for the gamma approximation to work well. + //x = qgamma(p, 0.5, 1.0); // qgamma(0.270614, 0.5, 1) = 0.05983807 + RealType q = quantile(g, p); + // cout << "quantile((g, p)) = " << q << endl;// 49.014664823030209 + //<< ", qgamma(1.- p, 0.5, 1.0); = " << x << endl; // 1.#INF + // x = mu * exp(q * static_cast(0.1)); // Said to improve at high p + // x = mu * x; // Improves at high p? + x = mu * exp(q / sqrt(phi) - 1/(2 * phi)); + } + } + return x; + } // guess_ig +} // namespace detail + +template +inline RealType quantile(const inverse_gaussian_distribution& dist, const RealType& p) +{ + BOOST_MATH_STD_USING // for ADL of std functions. + // No closed form exists so guess and use Newton Raphson iteration. + + RealType mean = dist.mean(); + RealType scale = dist.scale(); + static const char* function = "boost::math::quantile(const inverse_gaussian_distribution<%1%>&, %1%)"; + + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if(false == detail::check_probability(function, p, &result, Policy())) + return result; + if (p == 0) + { + return 0; // Convenient, even if not defined mathematically? + } + if (p == 1) + { // Might not return infinity? + return numeric_limits::infinity(); + } + //RealType guess_ig(RealType p, RealType mu = 1, RealType lambda = 1); + + RealType guess = detail::guess_ig(p, dist.mean(), dist.scale()); + using boost::math::tools::max_value; + + RealType min = 0.; // Minimum possible value is bottom of range of distribution. + RealType max = max_value();// Maximum possible value is top of range. + // int digits = std::numeric_limits::digits; // Maximum possible binary digits accuracy for type T. + // digits used to control how accurate to try to make the result. + // To allow user to control accuracy versus speed, + int get_digits = policies::digits();// get digits from policy, + boost::uintmax_t m = policies::get_max_root_iterations(); // and max iterations. + if(false) + { + cout << "Probability " << p << ", guess " << guess + << ", min " << min << ", max " << max + //<< ", std::numeric_limits<" << typeid(RealType).name() << ">::digits = " << digits + << ", accuracy " << get_digits << " bits." + << ", max iterations set by policy " << m + << endl; + } + using boost::math::tools::newton_raphson_iterate; + result = + newton_raphson_iterate(inverse_gaussian_quantile_functor(dist, p), guess, min, max, get_digits, m); + //cout << m << " iterations." << endl; + return result; +} // quantile + +template +inline RealType cdf(const complemented2_type, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = c.dist.scale(); + RealType mean = c.dist.mean(); + RealType x = c.param; + static const char* function = "boost::math::cdf(const complement(inverse_gaussian_distribution<%1%>&), %1%)"; + // infinite arguments not supported. + //if((boost::math::isinf)(x)) + //{ + // if(x < 0) return 1; // cdf complement -infinity is unity. + // return 0; // cdf complement +infinity is zero + //} + // These produce MSVC 4127 warnings, so the above used instead. + //if(std::numeric_limits::has_infinity && x == std::numeric_limits::infinity()) + //{ // cdf complement +infinity is zero. + // return 0; + //} + //if(std::numeric_limits::has_infinity && x == -std::numeric_limits::infinity()) + //{ // cdf complement -infinity is unity. + // return 1; + //} + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if(false == detail::check_x(function, x, &result, Policy())) + return result; + + normal_distribution n01; + RealType n0 = sqrt(scale / x); + n0 *= ((x / mean) -1); + RealType cdf_1 = cdf(complement(n01, n0)); + + RealType expfactor = exp(2 * scale / mean); + RealType n3 = - sqrt(scale / x); + n3 *= (x / mean) + 1; + + //RealType n5 = +sqrt(scale/x) * ((x /mean) + 1); // note now positive sign. + RealType n6 = cdf(complement(n01, +sqrt(scale/x) * ((x /mean) + 1))); + RealType n4 = cdf(n01, n3); // = + result = cdf_1 - expfactor * n6; + if(false) + { + cout <<"_\n cdf(complement ===========================" << endl; + cout << "sqrt(scale / x)*((x / mean) -1) = " << n0 << endl; + cout << "cdf(complement(n01, n1)) = " << cdf_1 << endl; + cout << "-sqrt(scale / x) * ((x / mean) +1) = " << n3 << endl; + cout << "exp(2 * scale / mean) = " << expfactor << endl; + cout << "cdf(complement(n01, +sqrt(scale/x) * ((x /mean) + 1))) = " << n6 << endl; + cout << "cdf((n01, ) exp(2 * scale / mean) * (x / mean) + 1) = " << n4 << endl; + cout << "exp * cdf_2 = " << result << endl; + } + //cout << "cdf(complement) result = " << result << endl; + return result; +} // cdf complement + +template +inline RealType quantile(const complemented2_type, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = c.dist.scale(); + RealType mean = c.dist.mean(); + static const char* function = "boost::math::quantile(const complement(inverse_gaussian_distribution<%1%>&), %1%)"; + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + RealType q = c.param; + if(false == detail::check_probability(function, q, &result, Policy())) + return result; + + RealType guess = detail::guess_ig(q, mean, scale); + // Complement. + using boost::math::tools::max_value; + + RealType min = 0.; // Minimum possible value is bottom of range of distribution. + RealType max = max_value();// Maximum possible value is top of range. + // int digits = std::numeric_limits::digits; // Maximum possible binary digits accuracy for type T. + // digits used to control how accurate to try to make the result. + int get_digits = policies::digits(); + boost::uintmax_t m = policies::get_max_root_iterations(); + if(false) + { + cout << "Probability " << q << ", guess at x = " << guess + //<< ", min " << min << ", max " << max + ////<< ", std::numeric_limits<" << typeid(RealType).name() << ">::digits = " << digits + // << ", accuracy " << get_digits << " bits." + // << ", max iterations set by policy " << m + << endl; + } + using boost::math::tools::newton_raphson_iterate; + result = + newton_raphson_iterate(inverse_gaussian_quantile_complement_functor(c.dist, q), guess, min, max, get_digits, m); + //cout << m << " iterations." << endl; + return result; +} // quantile + +template +inline RealType mean(const inverse_gaussian_distribution& dist) +{ // aka mu + return dist.mean(); +} + +template +inline RealType scale(const inverse_gaussian_distribution& dist) +{ // aka lambda + return dist.scale(); +} + +template +inline RealType shape(const inverse_gaussian_distribution& dist) +{ // aka phi + return dist.shape(); +} + +template +inline RealType standard_deviation(const inverse_gaussian_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = sqrt(mean * mean * mean / scale); + return result; +} + +template +inline RealType mode(const inverse_gaussian_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = mean * (sqrt(1 + (9 * mean * mean)/(4 * scale * scale)) + - 3 * mean / (2 * scale)); + return result; +} + +template +inline RealType skewness(const inverse_gaussian_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 3 * sqrt(mean/scale); + return result; +} + +template +inline RealType kurtosis(const inverse_gaussian_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 15 * mean / scale -3; + return result; +} + +template +inline RealType kurtosis_excess(const inverse_gaussian_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 15 * mean / scale; + return result; +} + +} // 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 + +#endif // BOOST_STATS_INVERSE_GAUSSIAN_HPP + + diff --git a/include/boost/math/distributions/inverse_normal.hpp b/include/boost/math/distributions/inverse_normal.hpp new file mode 100644 index 000000000..731d568de --- /dev/null +++ b/include/boost/math/distributions/inverse_normal.hpp @@ -0,0 +1,361 @@ +// Copyright John Maddock 2010. +// Copyright Paul A. Bristow 2010. + +// 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) + +#ifndef BOOST_STATS_INVERSE_NORMAL_HPP +#define BOOST_STATS_INVERSE_NORMAL_HPP + +// http://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution +// http://mathworld.wolfram.com/InverseGaussianDistribution.html + +// The normal-inverse Gaussian distribution (also called the Wald distribution when mean = 1) +// is the continuous probability distribution +// that is defined as the normal variance-mean mixture where the mixing density is the +// inverse Gaussian distribution. The tails of the distribution decrease more slowly +// than the normal distribution. It is therefore suitable to model phenomena +// where numerically large values are more probable than is the case for the normal distribution. + +// Examples are returns from financial assets and turbulent wind speeds. +// The normal-inverse Gaussian distributions form +// a subclass of the generalised hyperbolic distributions. + +// See also + +// http://en.wikipedia.org/wiki/Normal_distribution +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm +// Also: +// Weisstein, Eric W. "Normal Distribution." +// From MathWorld--A Wolfram Web Resource. +// http://mathworld.wolfram.com/NormalDistribution.html + +// http://www.jstatsoft.org/v26/i04/paper General class of inverse Gaussian distributions. +// ig package - withdrawn but at http://cran.r-project.org/src/contrib/Archive/ig/ + +// http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/SuppDists/html/invGauss.html +// R package for dinvGauss, ... + +#include +#include // for erf/erfc. +#include +#include +#include + +#include + +namespace boost{ namespace math{ + +template > +class inverse_normal_distribution +{ +public: + typedef RealType value_type; + typedef Policy policy_type; + + inverse_normal_distribution(RealType mean = 1, RealType sd = 1) + : m_mean(mean), m_sd(sd) + { // Default is a 1,1 inverse_normal distribution. + static const char* function = "boost::math::inverse_normal_distribution<%1%>::inverse_normal_distribution"; + + RealType result; + detail::check_scale(function, sd, &result, Policy()); + detail::check_location(function, mean, &result, Policy()); + } + + RealType mean()const + { // alias for location. + return m_mean; // aka mu + } + + RealType standard_deviation()const + { // alias for scale. + return m_sd; // aka lambda. + } + + // Synonyms, provided to allow generic use of find_location and find_scale. + RealType location()const + { // location, aka mu. + return m_mean; + } + RealType scale()const + { // scale, aka lambda. + return m_sd; + } + +private: + // + // Data members: + // + RealType m_mean; // distribution mean or location, aka mu. + RealType m_sd; // distribution standard deviation or scale, aka lambda. +}; // class normal_distribution + +typedef inverse_normal_distribution inverse_normal; + +template +inline const std::pair range(const inverse_normal_distribution& /*dist*/) +{ // Range of permissible values for random variable x, zero to max. + using boost::math::tools::max_value; + return std::pair(static_cast(0), max_value()); // - to + max value. +} + +template +inline const std::pair support(const inverse_normal_distribution& /*dist*/) +{ // Range of supported values for random variable x, zero to max. + // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. + + using boost::math::tools::max_value; + return std::pair(static_cast(0), max_value()); // - to + max value. +} + +template +inline RealType pdf(const inverse_normal_distribution& dist, const RealType& x) +{ // Probability Density Function + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result; + static const char* function = "boost::math::pdf(const inverse_normal_distribution<%1%>&, %1%)"; + if(false == detail::check_scale(function, scale, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if(false == detail::check_x_gt0(function, x, &result, Policy())) + { + return numeric_limits::quiet_NaN(); + } + + //result = + // sqrt(scale / (2 * constants::pi() * x * x * x)) + // * exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean)); + + result = + sqrt(scale / (constants::two_pi() * x * x * x)) + * exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean)); + return result; +} // pdf + +template +inline RealType cdf(const inverse_normal_distribution& dist, const RealType& x) +{ // Cumulative Density Function. + BOOST_MATH_STD_USING // for ADL of std functions + + RealType scale = dist.scale(); + RealType mean = dist.mean(); + static const char* function = "boost::math::cdf(const inverse_normal_distribution<%1%>&, %1%)"; + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + { + return result; + } + if(false == detail::check_location(function, mean, &result, Policy())) + { + return result; + } + if(false == detail::check_x_gt0(function, x, &result, Policy())) + { + return result; + } + + //result = 0.5 * (erf(sqrt(scale / x) * (x / mean -1) / sqrt(2.L), Policy()) + 1) + // + exp(2 * scale / mean) / 2 + // * (1 - erf(sqrt(scale / x) * (x / mean +1) / sqrt(2.L), Policy())); + + result = 0.5 * (erf(sqrt(scale / x) * (x / mean - 1) / constants::root_two(), Policy()) + 1) + + exp(2 * scale / mean) / 2 + * (1 - erf(sqrt(scale / x) * (x / mean + 1) / constants::root_two(), Policy())); + + return result; +} // cdf + +template +inline RealType quantile(const inverse_normal_distribution& dist, const RealType& x) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType mean = dist.mean(); + RealType scale = dist.scale(); + static const char* function = "boost::math::quantile(const inverse_normal_distribution<%1%>&, %1%)"; + + RealType result; + if(false == detail::check_scale(function, scale, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if(false == detail::check_probability(function, x, &result, Policy())) + return result; + + cout << "x " << x << endl; + RealType a = sqrt(scale / x); // a scale = lambda/x + RealType b = x / mean; // b = x/mu + + // pnorm q, mean, sd, lower.tail = true; + + //double q=1.0-pnorm(+a*(b-1.0), 0, 1, true, false); + //double p= pnorm(-a*(b+1.0), 0, 1, true, false); + + //boost::math::normal_distribution norm01; + using boost::math::normal; + normal norm01; + + double qx = a * (b - 1.0); + RealType q = 1 - ((qx <= 0) ? 0 : cdf(norm01, qx)); + cout << "a = " << a << ", b = " << b << ", qx = " << qx << ", pnorm= " << pnorm01(qx) << ", cdf= " << cdf(norm01, qx) << " q = " << q << endl; + + //cout << "1 - pnorm01(qx) " << 1.0 - pnorm01(qx) << endl; + + + + RealType px = -a * (b + 1.0); + RealType p = pnorm01(px); + RealType cdfpx = (px <= 0) ? 0 : cdf(norm01, px); + cout << "-a*(b+1.0) == px = " << px <<", pnorm01(p) = " << p << ", cdfpx = " << cdfpx << endl; + + if (p == 0) + { + result = q; + } + else + { + RealType r2 = 2 * scale / mean; + if (r2 >= numeric_limits::max() ) + { + result = numeric_limits::quiet_NaN(); + } + else + { + result = q - exp(r2) * p; + } + } + return result; +} // quantile + +template +inline RealType cdf(const complemented2_type, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = c.dist.standard_deviation(); + RealType mean = c.dist.mean(); + RealType x = c.param; + static const char* function = "boost::math::cdf(const complement(inverse_normal_distribution<%1%>&), %1%)"; + + if((boost::math::isinf)(x)) + { + if(x < 0) return 1; // cdf complement -infinity is unity. + return 0; // cdf complement +infinity is zero + } + // These produce MSVC 4127 warnings, so the above used instead. + //if(std::numeric_limits::has_infinity && x == std::numeric_limits::infinity()) + //{ // cdf complement +infinity is zero. + // return 0; + //} + //if(std::numeric_limits::has_infinity && x == -std::numeric_limits::infinity()) + //{ // cdf complement -infinity is unity. + // return 1; + //} + RealType result; + if(false == detail::check_scale(function, sd, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + if(false == detail::check_x(function, x, &result, Policy())) + return result; + + RealType diff = (x - mean) / (sd * constants::root_two()); + result = boost::math::erfc(diff, Policy()) / 2; + return result; +} // cdf complement + +template +inline RealType quantile(const complemented2_type, RealType>& c) +{ + BOOST_MATH_STD_USING // for ADL of std functions + + RealType sd = c.dist.standard_deviation(); + RealType mean = c.dist.mean(); + static const char* function = "boost::math::quantile(const complement(inverse_normal_distribution<%1%>&), %1%)"; + RealType result; + if(false == detail::check_scale(function, sd, &result, Policy())) + return result; + if(false == detail::check_location(function, mean, &result, Policy())) + return result; + RealType q = c.param; + if(false == detail::check_probability(function, q, &result, Policy())) + return result; + result = boost::math::erfc_inv(2 * q, Policy()); + result *= sd * constants::root_two(); + result += mean; + return result; +} // quantile + +template +inline RealType mean(const inverse_normal_distribution& dist) +{ + return dist.mean(); +} + +template +inline RealType standard_deviation(const inverse_normal_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = sqrt(mean * mean * mean / scale) + return result; +} + +template +inline RealType mode(const inverse_normal_distribution& dist) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = mean * (sqrt(1 + (9 * mean * mean)/(4 * scale * scale)) + - 3 * mean / (2 * scale)); + return result; +} + +template +inline RealType skewness(const inverse_normal_distribution& /*dist*/) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 3 * sqrt(mean/scale); + return result; +} + +template +inline RealType kurtosis(const inverse_normal_distribution& /*dist*/) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 12 * mean / scale ; + return result; +} + +template +inline RealType kurtosis_excess(const inverse_normal_distribution& /*dist*/) +{ + RealType scale = dist.scale(); + RealType mean = dist.mean(); + RealType result = 15 * mean / scale; + return result; +} + +} // 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 + +#endif // BOOST_STATS_INVERSE_NORMAL_HPP + + diff --git a/include/boost/math/distributions/inverse_uniform.hpp b/include/boost/math/distributions/inverse_uniform.hpp new file mode 100644 index 000000000..7ab097a6f --- /dev/null +++ b/include/boost/math/distributions/inverse_uniform.hpp @@ -0,0 +1,400 @@ +// Copyright John Maddock 2010. +// Copyright Paul A. Bristow 2010. +// 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) + +#ifndef BOOST_STATS_INVERSE_UNIFORM_HPP +#define BOOST_STATS_INVERSE_UNIFORM_HPP + +// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm +// http://mathworld.wolfram.com/UniformDistribution.html +// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/UniformDistribution.html +// http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 + +#include +#include +#include + +#include + +namespace boost{ namespace math +{ + namespace detail + { + template + inline bool check_inverse_uniform_lower( + const char* function, + RealType lower, + RealType* result, const Policy& pol) + { + if((boost::math::isfinite)(lower)) + { // any finite value is OK. + return true; + } + else + { // Not finite. + *result = policies::raise_domain_error( + function, + "Lower parameter is %1%, but must be >= 0!", lower, pol); + return false; + } + } // bool check_inverse_uniform_lower( + + template + inline bool check_inverse_uniform_upper( + const char* function, + RealType upper, + RealType* result, const Policy& pol) + { + if((boost::math::isfinite)(upper)) + { // Any finite value is OK. + return true; + } + else + { // Not finite. + *result = policies::raise_domain_error( + function, + "Upper parameter is %1%, but must be finite!", upper, pol); + return false; + } + } // bool check_inverse_uniform_upper( + + template + inline bool check_inverse_uniform_x( + const char* function, + RealType const& x, + RealType* result, const Policy& pol) + { + if((boost::math::isfinite)(x)) + { // Any finite value - if < lower or >upper will return NaN + return true; + } + else + { // Not finite.. + *result = policies::raise_domain_error( + function, + "y parameter is %1%, but must be finite!", x, pol); + return false; + } + } // bool check_inverse_uniform_x + + template + inline bool check_inverse_uniform( + const char* function, + RealType lower, + RealType upper, + RealType* result, const Policy& pol) + { + if((check_inverse_uniform_lower(function, lower, result, pol) == false) + || (check_inverse_uniform_upper(function, upper, result, pol) == false)) + { + return false; + } + else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity! + { // upper and lower have been checked before, so must be lower >= upper. + *result = policies::raise_domain_error( + function, + "lower parameter is %1%, but must be less than upper!", lower, pol); + return false; + } + else + { // All OK, + return true; + } + } // bool check_inverse_uniform( + + } // namespace detail + + template > + class inverse_uniform_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + inverse_uniform_distribution(RealType lower = 0, RealType upper = 1) // Constructor. + : m_lower(lower), m_upper(upper) // Default is standard uniform distribution. + { + RealType result; + detail::check_inverse_uniform( + "boost::math::inverse_uniform_distribution<%1%>::inverse_uniform_distribution", + lower, upper, &result, Policy()); + } + // Accessor functions. + RealType lower()const + { + return m_lower; + } + + RealType upper()const + { + return m_upper; + } + private: + // Data members: + RealType m_lower; // distribution lower aka a. + RealType m_upper; // distribution upper aka b. + }; // class inverse_uniform_distribution + + typedef inverse_uniform_distribution inverse_uniform; + + template + inline const std::pair range(const inverse_uniform_distribution& /* dist */) + { // Range of permissible values for random variable x. + using boost::math::tools::max_value; + return std::pair(dist.lower(), dist.upper()); // 0 to 1. + // Note RealType infinity is NOT permitted, only max_value. + } + + template + inline const std::pair support(const inverse_uniform_distribution& 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. + using boost::math::tools::max_value; + return std::pair(dist.lower(), dist.upper()); + } + + template + inline RealType pdf(const inverse_uniform_distribution& dist, const RealType& x) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform( + "boost::math::pdf(const inverse_uniform_distribution<%1%>&, %1%)", + lower, upper, &result, Policy())) + { + return result; + } + if(false == detail::check_inverse_uniform_x( + "boost::math::pdf(const inverse_uniform_distribution<%1%>&, %1%)", x, &result, Policy())) + { + return result; + } + // Undefined (singularity) outside lower to upper. + if((x < lower) || (x > upper) ) + { + return std::numeric_limits::quiet_NaN(); + } + else + { + return 1 / (upper - lower); + } + } // RealType pdf(const inverse_uniform_distribution& dist, const RealType& x) + + template + inline RealType cdf(const inverse_uniform_distribution& dist, const RealType& x) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform( + "boost::math::cdf(const inverse_uniform_distribution<%1%>&, %1%)", + lower, upper, &result, Policy())) + { + return result; + } + if(false == detail::check_inverse_uniform_x( + "boost::math::cdf(const inverse_uniform_distribution<%1%>&, %1%)", + x, &result, Policy())) + { + return result; + } + // Undefined (singularity) outside 0 to 1. + if (x < 0) + { + return std::numeric_limits::quiet_NaN(); + } + if (x > 1) + { + return std::numeric_limits::quiet_NaN(); + } + return x * (upper - lower) + lower; // lower <= x <= upper + } // RealType cdf(const inverse_uniform_distribution& dist, const RealType& x) + + template + inline RealType quantile(const inverse_uniform_distribution& dist, const RealType& p) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks + if(false == detail::check_inverse_uniform( + "boost::math::quantile(const inverse_uniform_distribution<%1%>&, %1%)", + lower, upper, &result, Policy())) + { + return result; + } + if(false == detail::check_probability( + "boost::math::quantile(const inverse_uniform_distribution<%1%>&, %1%)", + p, &result, Policy())) + { + return result; + } + if(p == 0) + { + return lower; + } + if(p == 1) + { + return upper; + } + return p * (upper - lower) + lower; + } // RealType quantile(const inverse_uniform_distribution& dist, const RealType& p) + + template + inline RealType cdf(const complemented2_type, RealType>& c) + { + RealType lower = c.dist.lower(); + RealType upper = c.dist.upper(); + RealType x = c.param; + RealType result; // of checks. + if(false == detail::check_inverse_uniform( + "boost::math::cdf(const inverse_uniform_distribution<%1%>&, %1%)", + lower, upper, &result, Policy())) + { + return result; + } + if(false == detail::check_inverse_uniform_x( + "boost::math::cdf(const inverse_uniform_distribution<%1%>&, %1%)", + x, &result, Policy())) + { + return result; + } + if (x < lower) + { + return 0; + } + if (x > upper) + { + return 1; + } + return (upper - x) / (upper - lower); + } // RealType cdf(const complemented2_type, RealType>& c) + + template + inline RealType quantile(const complemented2_type, RealType>& c) + { + RealType lower = c.dist.lower(); + RealType upper = c.dist.upper(); + RealType q = c.param; + RealType result; // of checks. + if(false == detail::check_inverse_uniform( + "boost::math::quantile(const inverse_uniform_distribution<%1%>&, %1%)", + lower, upper, &result, Policy())) + { + return result; + } + if(false == detail::check_probability( + "boost::math::quantile(const inverse_uniform_distribution<%1%>&, %1%)", + q, &result, Policy())) + if(q == 0) + { + return lower; + } + if(q == 1) + { + return upper; + } + return -q * (upper - lower) + upper; + } // RealType quantile(const complemented2_type, RealType>& c) + + template + inline RealType mean(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform( + "boost::math::mean(const inverse_uniform_distribution<%1%>&)", + lower, upper, &result, Policy())) + { + return result; + } + return (lower + upper ) / 2; + } // RealType mean(const inverse_uniform_distribution& dist) + + template + inline RealType variance(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform("boost::math::variance(const inverse_uniform_distribution<%1%>&)", lower, upper, &result, Policy())) + { + return result; + } + return (upper - lower) * ( upper - lower) / 12; + // for standard inverse_uniform = 0.833333333333333333333333333333333333333333; + } // RealType variance(const inverse_uniform_distribution& dist) + + template + inline RealType mode(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform("boost::math::mode(const inverse_uniform_distribution<%1%>&)", lower, upper, &result, Policy())) + { + return result; + } + result = lower; // Any value [lower, upper] but arbitrarily choose lower. + return result; + } + + template + inline RealType median(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform("boost::math::median(const inverse_uniform_distribution<%1%>&)", lower, upper, &result, Policy())) + { + return result; + } + return (lower + upper) / 2; // + } + template + inline RealType skewness(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform("boost::math::skewness(const inverse_uniform_distribution<%1%>&)",lower, upper, &result, Policy())) + { + return result; + } + return 0; + } // RealType skewness(const inverse_uniform_distribution& dist) + + template + inline RealType kurtosis_excess(const inverse_uniform_distribution& dist) + { + RealType lower = dist.lower(); + RealType upper = dist.upper(); + RealType result; // of checks. + if(false == detail::check_inverse_uniform("boost::math::kurtosis_execess(const inverse_uniform_distribution<%1%>&)", lower, upper, &result, Policy())) + { + return result; + } + return static_cast(-6)/5; // -6/5 = -1.2; + } // RealType kurtosis_excess(const inverse_uniform_distribution& dist) + + template + inline RealType kurtosis(const inverse_uniform_distribution& dist) + { + return kurtosis_excess(dist) + 3; + } + +} // 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 + +#endif // BOOST_STATS_INVERSE_UNIFORM_HPP + + +