532 lines
18 KiB
Plaintext
532 lines
18 KiB
Plaintext
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// Copyright John Maddock 2006, 2007.
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// Copyright Paul A. Bristow 2006, 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_STATS_TRIANGULAR_HPP
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#define BOOST_STATS_TRIANGULAR_HPP
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// http://mathworld.wolfram.com/TriangularDistribution.html
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// Note that the 'constructors' defined by Wolfram are difference from those here,
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// for example
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// N[variance[triangulardistribution{1, +2}, 1.5], 50] computes
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// 0.041666666666666666666666666666666666666666666666667
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// TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2)
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// http://en.wikipedia.org/wiki/Triangular_distribution
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/expm1.hpp>
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#include <boost/math/distributions/detail/common_error_handling.hpp>
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#include <boost/math/distributions/complement.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <utility>
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namespace boost{ namespace math
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{
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namespace detail
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{
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template <class RealType, class Policy>
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inline bool check_triangular_lower(
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const char* function,
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RealType lower,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(lower))
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{ // Any finite value is OK.
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return true;
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}
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else
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{ // Not finite: infinity or NaN.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Lower parameter is %1%, but must be finite!", lower, pol);
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return false;
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}
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} // bool check_triangular_lower(
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template <class RealType, class Policy>
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inline bool check_triangular_mode(
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const char* function,
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RealType mode,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(mode))
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{ // any finite value is OK.
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return true;
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}
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else
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{ // Not finite: infinity or NaN.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Mode parameter is %1%, but must be finite!", mode, pol);
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return false;
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}
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} // bool check_triangular_mode(
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template <class RealType, class Policy>
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inline bool check_triangular_upper(
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const char* function,
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RealType upper,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(upper))
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{ // any finite value is OK.
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return true;
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}
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else
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{ // Not finite: infinity or NaN.
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*result = policies::raise_domain_error<RealType>(
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function,
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"Upper parameter is %1%, but must be finite!", upper, pol);
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return false;
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}
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} // bool check_triangular_upper(
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template <class RealType, class Policy>
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inline bool check_triangular_x(
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const char* function,
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RealType const& x,
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RealType* result, const Policy& pol)
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{
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if((boost::math::isfinite)(x))
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{ // Any finite value is OK
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return true;
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}
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else
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{ // Not finite: infinity or NaN.
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*result = policies::raise_domain_error<RealType>(
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function,
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"x parameter is %1%, but must be finite!", x, pol);
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return false;
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}
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} // bool check_triangular_x
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template <class RealType, class Policy>
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inline bool check_triangular(
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const char* function,
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RealType lower,
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RealType mode,
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RealType upper,
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RealType* result, const Policy& pol)
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{
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if ((check_triangular_lower(function, lower, result, pol) == false)
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|| (check_triangular_mode(function, mode, result, pol) == false)
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|| (check_triangular_upper(function, upper, result, pol) == false))
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{ // Some parameter not finite.
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return false;
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}
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else if (lower >= upper) // lower == upper NOT useful.
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{ // lower >= upper.
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*result = policies::raise_domain_error<RealType>(
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function,
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"lower parameter is %1%, but must be less than upper!", lower, pol);
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return false;
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}
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else
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{ // Check lower <= mode <= upper.
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if (mode < lower)
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"mode parameter is %1%, but must be >= than lower!", lower, pol);
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return false;
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}
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if (mode > upper)
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"mode parameter is %1%, but must be <= than upper!", upper, pol);
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return false;
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}
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return true; // All OK.
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}
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} // bool check_triangular
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class triangular_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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triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
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: m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
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{ // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
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// has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
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// But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
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// where the central value is the most likely and deviations either side equally likely.
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RealType result;
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detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
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}
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// Accessor functions.
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RealType lower()const
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{
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return m_lower;
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}
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RealType mode()const
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{
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return m_mode;
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}
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RealType upper()const
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{
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return m_upper;
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}
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private:
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// Data members:
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RealType m_lower; // distribution lower aka a
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RealType m_mode; // distribution mode aka c
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RealType m_upper; // distribution upper aka b
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}; // class triangular_distribution
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typedef triangular_distribution<double> triangular;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
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{ // Range of permissible values for random variable x.
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
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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 triangular_distribution<RealType, Policy>& dist)
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{ // Range of supported values for random variable x.
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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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return std::pair<RealType, RealType>(dist.lower(), dist.upper());
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}
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template <class RealType, class Policy>
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RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
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{
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static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)";
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RealType lower = dist.lower();
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RealType mode = dist.mode();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_triangular_x(function, x, &result, Policy()))
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{
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return result;
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}
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if((x < lower) || (x > upper))
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{
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return 0;
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}
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if (x == lower)
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{ // (mode - lower) == 0 which would lead to divide by zero!
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return (mode == lower) ? 2 / (upper - lower) : RealType(0);
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}
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else if (x == upper)
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{
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return (mode == upper) ? 2 / (upper - lower) : RealType(0);
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}
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else if (x <= mode)
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{
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return 2 * (x - lower) / ((upper - lower) * (mode - lower));
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}
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else
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{ // (x > mode)
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return 2 * (upper - x) / ((upper - lower) * (upper - mode));
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}
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} // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
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template <class RealType, class Policy>
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inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
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{
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static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
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RealType lower = dist.lower();
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RealType mode = dist.mode();
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RealType upper = dist.upper();
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RealType result = 0; // of checks.
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if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_triangular_x(function, x, &result, Policy()))
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{
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return result;
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}
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if((x <= lower))
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{
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return 0;
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}
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if (x >= upper)
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{
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return 1;
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}
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// else lower < x < upper
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if (x <= mode)
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{
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return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
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}
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else
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{
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return 1 - (upper - x) * (upper - x) / ((upper - lower) * (upper - mode));
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}
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} // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
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template <class RealType, class Policy>
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RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
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{
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BOOST_MATH_STD_USING // for ADL of std functions (sqrt).
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static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
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RealType lower = dist.lower();
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RealType mode = dist.mode();
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RealType upper = dist.upper();
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RealType result = 0; // of checks
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if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_probability(function, p, &result, Policy()))
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{
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return result;
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}
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if(p == 0)
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{
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return lower;
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}
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if(p == 1)
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{
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return upper;
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}
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RealType p0 = (mode - lower) / (upper - lower);
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RealType q = 1 - p;
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if (p < p0)
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{
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result = sqrt((upper - lower) * (mode - lower) * p) + lower;
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}
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else if (p == p0)
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{
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result = mode;
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}
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else // p > p0
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{
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result = upper - sqrt((upper - lower) * (upper - mode) * q);
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}
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return result;
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} // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)
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template <class RealType, class Policy>
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RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
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{
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static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
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RealType lower = c.dist.lower();
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RealType mode = c.dist.mode();
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RealType upper = c.dist.upper();
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RealType x = c.param;
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RealType result = 0; // of checks.
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if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_triangular_x(function, x, &result, Policy()))
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{
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return result;
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}
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if (x <= lower)
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{
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return 1;
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}
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if (x >= upper)
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{
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return 0;
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}
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if (x <= mode)
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{
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return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
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}
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else
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{
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return (upper - x) * (upper - x) / ((upper - lower) * (upper - mode));
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}
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} // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
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template <class RealType, class Policy>
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RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // Aid ADL for sqrt.
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static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
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RealType l = c.dist.lower();
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RealType m = c.dist.mode();
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RealType u = c.dist.upper();
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RealType q = c.param; // probability 0 to 1.
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RealType result = 0; // of checks.
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if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
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{
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return result;
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}
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if(false == detail::check_probability(function, q, &result, Policy()))
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{
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return result;
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}
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if(q == 0)
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{
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return u;
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}
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if(q == 1)
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|
{
|
||
|
|
return l;
|
||
|
|
}
|
||
|
|
RealType lower = c.dist.lower();
|
||
|
|
RealType mode = c.dist.mode();
|
||
|
|
RealType upper = c.dist.upper();
|
||
|
|
|
||
|
|
RealType p = 1 - q;
|
||
|
|
RealType p0 = (mode - lower) / (upper - lower);
|
||
|
|
if(p < p0)
|
||
|
|
{
|
||
|
|
RealType s = (upper - lower) * (mode - lower);
|
||
|
|
s *= p;
|
||
|
|
result = sqrt((upper - lower) * (mode - lower) * p) + lower;
|
||
|
|
}
|
||
|
|
else if (p == p0)
|
||
|
|
{
|
||
|
|
result = mode;
|
||
|
|
}
|
||
|
|
else // p > p0
|
||
|
|
{
|
||
|
|
result = upper - sqrt((upper - lower) * (upper - mode) * q);
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
} // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return (lower + upper + mode) / 3;
|
||
|
|
} // RealType mean(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
|
||
|
|
} // RealType variance(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
|
||
|
|
{ // This should never happen!
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return mode;
|
||
|
|
} // RealType mode
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType median(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING // ADL of std functions.
|
||
|
|
static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
|
||
|
|
{ // This should never happen!
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
if (mode >= (upper + lower) / 2)
|
||
|
|
{
|
||
|
|
return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
|
||
|
|
}
|
||
|
|
} // RealType mode
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
||
|
|
using namespace boost::math::constants; // for root_two
|
||
|
|
static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";
|
||
|
|
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
|
||
|
|
(5 * pow((lower * lower + upper * upper + mode * mode
|
||
|
|
- lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
|
||
|
|
// #11768: Skewness formula for triangular distribution is incorrect - corrected 29 Oct 2015 for release 1.61.
|
||
|
|
} // RealType skewness(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{ // These checks may be belt and braces as should have been checked on construction?
|
||
|
|
static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return static_cast<RealType>(12)/5; // 12/5 = 2.4;
|
||
|
|
} // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
|
||
|
|
{ // These checks may be belt and braces as should have been checked on construction?
|
||
|
|
static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
|
||
|
|
RealType lower = dist.lower();
|
||
|
|
RealType upper = dist.upper();
|
||
|
|
RealType mode = dist.mode();
|
||
|
|
RealType result = 0; // of checks.
|
||
|
|
if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
|
||
|
|
{
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
|
||
|
|
// Assuming mathworld really means kurtosis excess? Wikipedia now corrected to match this.
|
||
|
|
}
|
||
|
|
|
||
|
|
} // 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_TRIANGULAR_HPP
|
||
|
|
|
||
|
|
|
||
|
|
|