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Added new distributions.
[SVN r66728]
This commit is contained in:
Paul A. Bristow
516
include/boost/math/distributions/geometric.hpp
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516
include/boost/math/distributions/geometric.hpp
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// boost\math\distributions\geometric.hpp
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// Copyright John Maddock 2010.
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// Copyright Paul A. Bristow 2010.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// geometric distribution is a discrete probability distribution.
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// It expresses the probability distribution of the number (k) of
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// events, occurrences, failures or arrivals before the first success.
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// supported on the set {0, 1, 2, 3...}
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// Note that the set includes zero (unlike some definitions that start at one).
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// The random variate k is the number of events, occurrences or arrivals.
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// k argument may be integral, signed, or unsigned, or floating point.
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// If necessary, it has already been promoted from an integral type.
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// Note that the geometric distribution
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// (like others including the binomial, geometric & Bernoulli)
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// is strictly defined as a discrete function:
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// only integral values of k are envisaged.
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// However because the method of calculation uses a continuous gamma function,
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// it is convenient to treat it as if a continous function,
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// and permit non-integral values of k.
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// To enforce the strict mathematical model, users should use floor or ceil functions
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// on k outside this function to ensure that k is integral.
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// See http://en.wikipedia.org/wiki/geometric_distribution
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// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html
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// http://mathworld.wolfram.com/GeometricDistribution.html
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#ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP
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#define BOOST_MATH_SPECIAL_GEOMETRIC_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b).
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#include <boost/math/distributions/complement.hpp> // complement.
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#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error.
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#include <boost/math/special_functions/fpclassify.hpp> // isnan.
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#include <boost/math/tools/roots.hpp> // for root finding.
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#include <boost/math/distributions/detail/inv_discrete_quantile.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include <boost/type_traits/is_integral.hpp>
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#include <boost/type_traits/is_same.hpp>
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#include <boost/mpl/if.hpp>
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#include <limits> // using std::numeric_limits;
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#include <utility>
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#if defined (BOOST_MSVC)
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# pragma warning(push)
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// This believed not now necessary, so commented out.
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//# pragma warning(disable: 4702) // unreachable code.
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// in domain_error_imp in error_handling.
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#endif
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namespace boost
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{
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namespace math
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{
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namespace geometric_detail
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{
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// Common error checking routines for geometric distribution function:
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template <class RealType, class Policy>
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inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol)
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{
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if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) )
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol);
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return false;
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}
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol)
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{
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return check_success_fraction(function, p, result, pol);
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}
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template <class RealType, class Policy>
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inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol)
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{
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if(check_dist(function, p, result, pol) == false)
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{
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return false;
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}
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if( !(boost::math::isfinite)(k) || (k < 0) )
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{ // Check k failures.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Number of failures argument is %1%, but must be >= 0 !", k, pol);
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return false;
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}
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return true;
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} // Check_dist_and_k
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template <class RealType, class Policy>
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inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol)
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{
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if(check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol) == false)
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{
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return false;
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}
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return true;
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} // check_dist_and_prob
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} // namespace geometric_detail
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template <class RealType = double, class Policy = policies::policy<> >
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class geometric_distribution
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{
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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geometric_distribution(RealType p) : m_p(p)
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{ // Constructor stores success_fraction p.
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RealType result;
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geometric_detail::check_dist(
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"geometric_distribution<%1%>::geometric_distribution",
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m_p, // Check success_fraction 0 <= p <= 1.
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&result, Policy());
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} // geometric_distribution constructor.
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// Private data getter class member functions.
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RealType success_fraction() const
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{ // Probability of success as fraction in range 0 to 1.
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return m_p;
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}
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RealType successes() const
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{ // Total number of successes r = 1 (for compatibility with negative binomial?).
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return 1;
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}
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// Parameter estimation.
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// (These are copies of negative_binomial distribution with successes = 1).
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static RealType find_lower_bound_on_p(
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RealType trials,
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RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
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{
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static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p";
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RealType result; // of error checks.
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RealType successes = 1;
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RealType failures = trials - successes;
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if(false == detail::check_probability(function, alpha, &result, Policy())
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&& geometric_detail::check_dist_and_k(
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function, RealType(0), failures, &result, Policy()))
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{
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return result;
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}
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// Use complement ibeta_inv function for lower bound.
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// This is adapted from the corresponding binomial formula
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// here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
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// This is a Clopper-Pearson interval, and may be overly conservative,
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// see also "A Simple Improved Inferential Method for Some
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// Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY
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// http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
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//
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return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy());
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} // find_lower_bound_on_p
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static RealType find_upper_bound_on_p(
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RealType trials,
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RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test.
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{
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static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p";
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RealType result; // of error checks.
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RealType successes = 1;
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RealType failures = trials - successes;
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if(false == geometric_detail::check_dist_and_k(
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function, RealType(0), failures, &result, Policy())
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&& detail::check_probability(function, alpha, &result, Policy()))
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{
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return result;
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}
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if(failures == 0)
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{
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return 1;
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}// Use complement ibetac_inv function for upper bound.
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// Note adjusted failures value: *not* failures+1 as usual.
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// This is adapted from the corresponding binomial formula
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// here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
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// This is a Clopper-Pearson interval, and may be overly conservative,
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// see also "A Simple Improved Inferential Method for Some
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// Discrete Distributions" Yong CAI and K. Krishnamoorthy
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// http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf
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//
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return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy());
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} // find_upper_bound_on_p
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// Estimate number of trials :
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// "How many trials do I need to be P% sure of seeing k or fewer failures?"
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static RealType find_minimum_number_of_trials(
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RealType k, // number of failures (k >= 0).
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RealType p, // success fraction 0 <= p <= 1.
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RealType alpha) // risk level threshold 0 <= alpha <= 1.
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{
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static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials";
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// Error checks:
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RealType result;
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if(false == geometric_detail::check_dist_and_k(
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function, p, k, &result, Policy())
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&& detail::check_probability(function, alpha, &result, Policy()))
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{
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return result;
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}
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result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k
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return result + k;
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} // RealType find_number_of_failures
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static RealType find_maximum_number_of_trials(
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RealType k, // number of failures (k >= 0).
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RealType p, // success fraction 0 <= p <= 1.
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RealType alpha) // risk level threshold 0 <= alpha <= 1.
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{
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static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials";
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// Error checks:
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RealType result;
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if(false == geometric_detail::check_dist_and_k(
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function, p, k, &result, Policy())
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&& detail::check_probability(function, alpha, &result, Policy()))
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{
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return result;
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}
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result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k
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return result + k;
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} // RealType find_number_of_trials complemented
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private:
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//RealType m_r; // successes fixed at unity.
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RealType m_p; // success_fraction
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}; // template <class RealType, class Policy> class geometric_distribution
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typedef geometric_distribution<double> geometric; // Reserved name of type double.
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const geometric_distribution<RealType, Policy>& /* dist */)
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{ // Range of permissible values for random variable k.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer?
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}
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> support(const geometric_distribution<RealType, Policy>& /* dist */)
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{ // Range of supported values for random variable k.
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// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer?
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}
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template <class RealType, class Policy>
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inline RealType mean(const geometric_distribution<RealType, Policy>& dist)
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{ // Mean of geometric distribution = (1-p)/p.
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return (1 - dist.success_fraction() ) / dist.success_fraction();
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} // mean
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// median implemented via quantile(half) in derived accessors.
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template <class RealType, class Policy>
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inline RealType mode(const geometric_distribution<RealType, Policy>&)
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{ // Mode of geometric distribution = zero.
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BOOST_MATH_STD_USING // ADL of std functions.
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return 0;
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} // mode
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template <class RealType, class Policy>
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inline RealType variance(const geometric_distribution<RealType, Policy>& dist)
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{ // Variance of Binomial distribution = (1-p) / p^2.
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return (1 - dist.success_fraction())
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/ (dist.success_fraction() * dist.success_fraction());
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} // variance
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template <class RealType, class Policy>
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inline RealType skewness(const geometric_distribution<RealType, Policy>& dist)
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{ // skewness of geometric distribution = 2-p / (sqrt(r(1-p))
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BOOST_MATH_STD_USING // ADL of std functions.
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RealType p = dist.success_fraction();
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return (2 - p) / sqrt(1 - p);
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} // skewness
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template <class RealType, class Policy>
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inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist)
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{ // kurtosis of geometric distribution
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// http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3
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RealType p = dist.success_fraction();
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return 3 + (p*p - 6*p + 6) / (1 - p);
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} // kurtosis
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist)
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{ // kurtosis excess of geometric distribution
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// http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess
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RealType p = dist.success_fraction();
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return (p*p - 6*p + 6) / (1 - p);
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} // kurtosis_excess
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// RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist)
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// standard_deviation provided by derived accessors.
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// RealType hazard(const geometric_distribution<RealType, Policy>& dist)
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// hazard of geometric distribution provided by derived accessors.
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// RealType chf(const geometric_distribution<RealType, Policy>& dist)
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// chf of geometric distribution provided by derived accessors.
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template <class RealType, class Policy>
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inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
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{ // Probability Density/Mass Function.
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BOOST_FPU_EXCEPTION_GUARD
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BOOST_MATH_STD_USING // For ADL of math functions.
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static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)";
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RealType p = dist.success_fraction();
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RealType result;
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if(false == geometric_detail::check_dist_and_k(
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function,
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p,
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k,
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&result, Policy()))
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{
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return result;
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}
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if (k == 0)
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{
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return p; // success_fraction
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}
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RealType q = 1 - p; // Inaccurate for small p?
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// So try to avoid inaccuracy for large or small p.
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// but has little effect > last significant bit.
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//cout << "p * pow(q, k) " << result << endl; // seems best whatever p
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//cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl;
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//if (p < 0.5)
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//{
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// result = p * pow(q, k);
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//}
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//else
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//{
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// result = p * exp(k * log1p(-p));
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//}
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result = p * pow(q, k);
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return result;
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} // geometric_pdf
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template <class RealType, class Policy>
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inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k)
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{ // Cumulative Distribution Function of geometric.
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static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
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// k argument may be integral, signed, or unsigned, or floating point.
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// If necessary, it has already been promoted from an integral type.
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RealType p = dist.success_fraction();
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// Error check:
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RealType result;
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if(false == geometric_detail::check_dist_and_k(
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function,
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p,
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k,
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&result, Policy()))
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{
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return result;
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}
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if(k == 0)
|
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{
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return p; // success_fraction
|
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}
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//RealType q = 1 - p; // Bad for small p
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//RealType probability = 1 - std::pow(q, k+1);
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RealType z = log1p(-p) * (k+1);
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RealType probability = -expm1(z);
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return probability;
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} // cdf Cumulative Distribution Function geometric.
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c)
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{ // Complemented Cumulative Distribution Function geometric.
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static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)";
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// k argument may be integral, signed, or unsigned, or floating point.
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// If necessary, it has already been promoted from an integral type.
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RealType const& k = c.param;
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geometric_distribution<RealType, Policy> const& dist = c.dist;
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RealType p = dist.success_fraction();
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// Error check:
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RealType result;
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if(false == geometric_detail::check_dist_and_k(
|
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function,
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p,
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k,
|
||||
&result, Policy()))
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{
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return result;
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||||
}
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||||
RealType z = log1p(-p) * (k+1);
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||||
RealType probability = exp(z);
|
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return probability;
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} // cdf Complemented Cumulative Distribution Function geometric.
|
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||||
template <class RealType, class Policy>
|
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inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x)
|
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{ // 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.
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||||
|
||||
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<RealType>(
|
||||
function,
|
||||
"Probability argument is 1, which implies infinite failures !", Policy());
|
||||
return result;
|
||||
// usually means return +std::numeric_limits<RealType>::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 <class RealType, class Policy>
|
||||
inline RealType quantile(const complemented2_type<geometric_distribution<RealType, Policy>, 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<RealType, Policy>& 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<RealType>(
|
||||
function,
|
||||
"Probability argument complement is 0, which implies infinite failures !", Policy());
|
||||
return result;
|
||||
// usually means return +std::numeric_limits<RealType>::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 <boost/math/distributions/detail/derived_accessors.hpp>
|
||||
|
||||
#if defined (BOOST_MSVC)
|
||||
# pragma warning(pop)
|
||||
#endif
|
||||
|
||||
#endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP
|
||||
578
include/boost/math/distributions/inverse_gaussian.hpp
Normal file
578
include/boost/math/distributions/inverse_gaussian.hpp
Normal file
@@ -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 <boost/math/distributions/fwd.hpp>
|
||||
#include <boost/math/special_functions/erf.hpp> // for erf/erfc.
|
||||
#include <boost/math/distributions/complement.hpp>
|
||||
#include <boost/math/distributions/detail/common_error_handling.hpp>
|
||||
#include <boost/math/distributions/normal.hpp>
|
||||
#include <boost/math/distributions/gamma.hpp> // for gamma function
|
||||
// using boost::math::gamma_p;
|
||||
|
||||
#include <boost/math/tr1.hpp>
|
||||
//using std::tr1::tuple;
|
||||
//using std::tr1::make_tuple;
|
||||
#include <boost/math/tools/roots.hpp>
|
||||
//using boost::math::tools::newton_raphson_iterate;
|
||||
|
||||
#include <utility>
|
||||
|
||||
namespace boost{ namespace math{
|
||||
|
||||
template <class RealType = double, class Policy = policies::policy<> >
|
||||
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<double> inverse_gaussian;
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> range(const inverse_gaussian_distribution<RealType, Policy>& /*dist*/)
|
||||
{ // Range of permissible values for random variable x, zero to max.
|
||||
using boost::math::tools::max_value;
|
||||
return std::pair<RealType, RealType>(static_cast<RealType>(0.), max_value<RealType>()); // - to + max value.
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> support(const inverse_gaussian_distribution<RealType, Policy>& /*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<RealType, RealType>(static_cast<RealType>(0.), max_value<RealType>()); // - to + max value.
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType pdf(const inverse_gaussian_distribution<RealType, Policy>& 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<RealType>::quiet_NaN();
|
||||
}
|
||||
|
||||
if (x == 0)
|
||||
{
|
||||
return 0; // Convenient, even if not defined mathematically.
|
||||
}
|
||||
|
||||
result =
|
||||
sqrt(scale / (constants::two_pi<RealType>() * x * x * x))
|
||||
* exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean));
|
||||
return result;
|
||||
} // pdf
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const inverse_gaussian_distribution<RealType, Policy>& 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<RealType>(), Policy()) + 1)
|
||||
// + exp(2 * scale / mean) / 2
|
||||
// * (1 - erf(sqrt(scale / x) * (x / mean + 1) / constants::root_two<RealType>(), Policy()));
|
||||
// so use normal distribution version:
|
||||
// Wikipedia CDF equation http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution.
|
||||
|
||||
normal_distribution<RealType> 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 <class RealType>
|
||||
struct inverse_gaussian_quantile_functor
|
||||
{
|
||||
|
||||
inverse_gaussian_quantile_functor(const boost::math::inverse_gaussian_distribution<RealType> dist, RealType const& p)
|
||||
: distribution(dist), prob(p)
|
||||
{
|
||||
}
|
||||
boost::math::tuple<RealType, RealType> 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<RealType> distribution;
|
||||
RealType prob;
|
||||
};
|
||||
|
||||
template <class RealType>
|
||||
struct inverse_gaussian_quantile_complement_functor
|
||||
{
|
||||
inverse_gaussian_quantile_complement_functor(const boost::math::inverse_gaussian_distribution<RealType> dist, RealType const& p)
|
||||
: distribution(dist), prob(p)
|
||||
{
|
||||
}
|
||||
boost::math::tuple<RealType, RealType> 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<RealType>::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<RealType> distribution;
|
||||
RealType prob;
|
||||
};
|
||||
|
||||
namespace detail
|
||||
{
|
||||
template <class RealType>
|
||||
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_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<RealType, no_overthrow_policy> 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<RealType, no_overthrow_policy> gamma_nooverflow;
|
||||
|
||||
gamma_distribution<RealType, no_overthrow_policy> g(static_cast<RealType>(0.5), static_cast<RealType>(1.));
|
||||
|
||||
// gamma_nooverflow g(static_cast<RealType>(0.5), static_cast<RealType>(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<RealType>(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 <class RealType, class Policy>
|
||||
inline RealType quantile(const inverse_gaussian_distribution<RealType, Policy>& 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<RealType>::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<RealType>();// Maximum possible value is top of range.
|
||||
// int digits = std::numeric_limits<RealType>::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<RealType, Policy>();// get digits from policy,
|
||||
boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // 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<RealType>(dist, p), guess, min, max, get_digits, m);
|
||||
//cout << m << " iterations." << endl;
|
||||
return result;
|
||||
} // quantile
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const complemented2_type<inverse_gaussian_distribution<RealType, Policy>, 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<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
|
||||
//{ // cdf complement +infinity is zero.
|
||||
// return 0;
|
||||
//}
|
||||
//if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::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<RealType> 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 <class RealType, class Policy>
|
||||
inline RealType quantile(const complemented2_type<inverse_gaussian_distribution<RealType, Policy>, 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<RealType>();// Maximum possible value is top of range.
|
||||
// int digits = std::numeric_limits<RealType>::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<RealType, Policy>();
|
||||
boost::uintmax_t m = policies::get_max_root_iterations<Policy>();
|
||||
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<RealType>(c.dist, q), guess, min, max, get_digits, m);
|
||||
//cout << m << " iterations." << endl;
|
||||
return result;
|
||||
} // quantile
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mean(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{ // aka mu
|
||||
return dist.mean();
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType scale(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{ // aka lambda
|
||||
return dist.scale();
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType shape(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{ // aka phi
|
||||
return dist.shape();
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType standard_deviation(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = sqrt(mean * mean * mean / scale);
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mode(const inverse_gaussian_distribution<RealType, Policy>& 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 <class RealType, class Policy>
|
||||
inline RealType skewness(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = 3 * sqrt(mean/scale);
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis(const inverse_gaussian_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = 15 * mean / scale -3;
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis_excess(const inverse_gaussian_distribution<RealType, Policy>& 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 <boost/math/distributions/detail/derived_accessors.hpp>
|
||||
|
||||
#endif // BOOST_STATS_INVERSE_GAUSSIAN_HPP
|
||||
|
||||
|
||||
361
include/boost/math/distributions/inverse_normal.hpp
Normal file
361
include/boost/math/distributions/inverse_normal.hpp
Normal file
@@ -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 <boost/math/distributions/fwd.hpp>
|
||||
#include <boost/math/special_functions/erf.hpp> // for erf/erfc.
|
||||
#include <boost/math/distributions/complement.hpp>
|
||||
#include <boost/math/distributions/detail/common_error_handling.hpp>
|
||||
#include <boost/math/distributions/normal.hpp>
|
||||
|
||||
#include <utility>
|
||||
|
||||
namespace boost{ namespace math{
|
||||
|
||||
template <class RealType = double, class Policy = policies::policy<> >
|
||||
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<double> inverse_normal;
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> range(const inverse_normal_distribution<RealType, Policy>& /*dist*/)
|
||||
{ // Range of permissible values for random variable x, zero to max.
|
||||
using boost::math::tools::max_value;
|
||||
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // - to + max value.
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> support(const inverse_normal_distribution<RealType, Policy>& /*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<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // - to + max value.
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType pdf(const inverse_normal_distribution<RealType, Policy>& 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<RealType>::quiet_NaN();
|
||||
}
|
||||
|
||||
//result =
|
||||
// sqrt(scale / (2 * constants::pi<RealType>() * x * x * x))
|
||||
// * exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean));
|
||||
|
||||
result =
|
||||
sqrt(scale / (constants::two_pi<RealType>() * x * x * x))
|
||||
* exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean));
|
||||
return result;
|
||||
} // pdf
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const inverse_normal_distribution<RealType, Policy>& 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<RealType>(), Policy()) + 1)
|
||||
+ exp(2 * scale / mean) / 2
|
||||
* (1 - erf(sqrt(scale / x) * (x / mean + 1) / constants::root_two<RealType>(), Policy()));
|
||||
|
||||
return result;
|
||||
} // cdf
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType quantile(const inverse_normal_distribution<RealType, Policy>& 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<RealType> 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<RealType>::max() )
|
||||
{
|
||||
result = numeric_limits<RealType>::quiet_NaN();
|
||||
}
|
||||
else
|
||||
{
|
||||
result = q - exp(r2) * p;
|
||||
}
|
||||
}
|
||||
return result;
|
||||
} // quantile
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const complemented2_type<inverse_normal_distribution<RealType, Policy>, 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<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
|
||||
//{ // cdf complement +infinity is zero.
|
||||
// return 0;
|
||||
//}
|
||||
//if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::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<RealType>());
|
||||
result = boost::math::erfc(diff, Policy()) / 2;
|
||||
return result;
|
||||
} // cdf complement
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType quantile(const complemented2_type<inverse_normal_distribution<RealType, Policy>, 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<RealType>();
|
||||
result += mean;
|
||||
return result;
|
||||
} // quantile
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mean(const inverse_normal_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
return dist.mean();
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType standard_deviation(const inverse_normal_distribution<RealType, Policy>& dist)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = sqrt(mean * mean * mean / scale)
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mode(const inverse_normal_distribution<RealType, Policy>& 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 <class RealType, class Policy>
|
||||
inline RealType skewness(const inverse_normal_distribution<RealType, Policy>& /*dist*/)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = 3 * sqrt(mean/scale);
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis(const inverse_normal_distribution<RealType, Policy>& /*dist*/)
|
||||
{
|
||||
RealType scale = dist.scale();
|
||||
RealType mean = dist.mean();
|
||||
RealType result = 12 * mean / scale ;
|
||||
return result;
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis_excess(const inverse_normal_distribution<RealType, Policy>& /*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 <boost/math/distributions/detail/derived_accessors.hpp>
|
||||
|
||||
#endif // BOOST_STATS_INVERSE_NORMAL_HPP
|
||||
|
||||
|
||||
400
include/boost/math/distributions/inverse_uniform.hpp
Normal file
400
include/boost/math/distributions/inverse_uniform.hpp
Normal file
@@ -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 <boost/math/distributions/fwd.hpp>
|
||||
#include <boost/math/distributions/detail/common_error_handling.hpp>
|
||||
#include <boost/math/distributions/complement.hpp>
|
||||
|
||||
#include <utility>
|
||||
|
||||
namespace boost{ namespace math
|
||||
{
|
||||
namespace detail
|
||||
{
|
||||
template <class RealType, class Policy>
|
||||
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<RealType>(
|
||||
function,
|
||||
"Lower parameter is %1%, but must be >= 0!", lower, pol);
|
||||
return false;
|
||||
}
|
||||
} // bool check_inverse_uniform_lower(
|
||||
|
||||
template <class RealType, class Policy>
|
||||
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<RealType>(
|
||||
function,
|
||||
"Upper parameter is %1%, but must be finite!", upper, pol);
|
||||
return false;
|
||||
}
|
||||
} // bool check_inverse_uniform_upper(
|
||||
|
||||
template <class RealType, class Policy>
|
||||
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<RealType>(
|
||||
function,
|
||||
"y parameter is %1%, but must be finite!", x, pol);
|
||||
return false;
|
||||
}
|
||||
} // bool check_inverse_uniform_x
|
||||
|
||||
template <class RealType, class Policy>
|
||||
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<RealType>(
|
||||
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 RealType = double, class Policy = policies::policy<> >
|
||||
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<double> inverse_uniform;
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> range(const inverse_uniform_distribution<RealType, Policy>& /* dist */)
|
||||
{ // Range of permissible values for random variable x.
|
||||
using boost::math::tools::max_value;
|
||||
return std::pair<RealType, RealType>(dist.lower(), dist.upper()); // 0 to 1.
|
||||
// Note RealType infinity is NOT permitted, only max_value.
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline const std::pair<RealType, RealType> support(const inverse_uniform_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.
|
||||
using boost::math::tools::max_value;
|
||||
return std::pair<RealType, RealType>(dist.lower(), dist.upper());
|
||||
}
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType pdf(const inverse_uniform_distribution<RealType, Policy>& 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<RealType>::quiet_NaN();
|
||||
}
|
||||
else
|
||||
{
|
||||
return 1 / (upper - lower);
|
||||
}
|
||||
} // RealType pdf(const inverse_uniform_distribution<RealType, Policy>& dist, const RealType& x)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const inverse_uniform_distribution<RealType, Policy>& 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<RealType>::quiet_NaN();
|
||||
}
|
||||
if (x > 1)
|
||||
{
|
||||
return std::numeric_limits<RealType>::quiet_NaN();
|
||||
}
|
||||
return x * (upper - lower) + lower; // lower <= x <= upper
|
||||
} // RealType cdf(const inverse_uniform_distribution<RealType, Policy>& dist, const RealType& x)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType quantile(const inverse_uniform_distribution<RealType, Policy>& 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<RealType, Policy>& dist, const RealType& p)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType cdf(const complemented2_type<inverse_uniform_distribution<RealType, Policy>, 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<inverse_uniform_distribution<RealType, Policy>, RealType>& c)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType quantile(const complemented2_type<inverse_uniform_distribution<RealType, Policy>, 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<inverse_uniform_distribution<RealType, Policy>, RealType>& c)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mean(const inverse_uniform_distribution<RealType, Policy>& 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<RealType, Policy>& dist)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType variance(const inverse_uniform_distribution<RealType, Policy>& 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<RealType, Policy>& dist)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType mode(const inverse_uniform_distribution<RealType, Policy>& 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 <class RealType, class Policy>
|
||||
inline RealType median(const inverse_uniform_distribution<RealType, Policy>& 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 <class RealType, class Policy>
|
||||
inline RealType skewness(const inverse_uniform_distribution<RealType, Policy>& 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<RealType, Policy>& dist)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis_excess(const inverse_uniform_distribution<RealType, Policy>& 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<RealType>(-6)/5; // -6/5 = -1.2;
|
||||
} // RealType kurtosis_excess(const inverse_uniform_distribution<RealType, Policy>& dist)
|
||||
|
||||
template <class RealType, class Policy>
|
||||
inline RealType kurtosis(const inverse_uniform_distribution<RealType, Policy>& 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 <boost/math/distributions/detail/derived_accessors.hpp>
|
||||
|
||||
#endif // BOOST_STATS_INVERSE_UNIFORM_HPP
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user