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Boost-for-Android-Prebuilt/boost-1_72_0/include/boost/math/distributions/triangular.hpp

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// Copyright John Maddock 2006, 2007.
// Copyright Paul A. Bristow 2006, 2007.
// 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_TRIANGULAR_HPP
#define BOOST_STATS_TRIANGULAR_HPP
// http://mathworld.wolfram.com/TriangularDistribution.html
// Note that the 'constructors' defined by Wolfram are difference from those here,
// for example
// N[variance[triangulardistribution{1, +2}, 1.5], 50] computes
// 0.041666666666666666666666666666666666666666666666667
// TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2)
// http://en.wikipedia.org/wiki/Triangular_distribution
#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/math/distributions/complement.hpp>
#include <boost/math/constants/constants.hpp>
#include <utility>
namespace boost{ namespace math
{
namespace detail
{
template <class RealType, class Policy>
inline bool check_triangular_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: infinity or NaN.
*result = policies::raise_domain_error<RealType>(
function,
"Lower parameter is %1%, but must be finite!", lower, pol);
return false;
}
} // bool check_triangular_lower(
template <class RealType, class Policy>
inline bool check_triangular_mode(
const char* function,
RealType mode,
RealType* result, const Policy& pol)
{
if((boost::math::isfinite)(mode))
{ // any finite value is OK.
return true;
}
else
{ // Not finite: infinity or NaN.
*result = policies::raise_domain_error<RealType>(
function,
"Mode parameter is %1%, but must be finite!", mode, pol);
return false;
}
} // bool check_triangular_mode(
template <class RealType, class Policy>
inline bool check_triangular_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: infinity or NaN.
*result = policies::raise_domain_error<RealType>(
function,
"Upper parameter is %1%, but must be finite!", upper, pol);
return false;
}
} // bool check_triangular_upper(
template <class RealType, class Policy>
inline bool check_triangular_x(
const char* function,
RealType const& x,
RealType* result, const Policy& pol)
{
if((boost::math::isfinite)(x))
{ // Any finite value is OK
return true;
}
else
{ // Not finite: infinity or NaN.
*result = policies::raise_domain_error<RealType>(
function,
"x parameter is %1%, but must be finite!", x, pol);
return false;
}
} // bool check_triangular_x
template <class RealType, class Policy>
inline bool check_triangular(
const char* function,
RealType lower,
RealType mode,
RealType upper,
RealType* result, const Policy& pol)
{
if ((check_triangular_lower(function, lower, result, pol) == false)
|| (check_triangular_mode(function, mode, result, pol) == false)
|| (check_triangular_upper(function, upper, result, pol) == false))
{ // Some parameter not finite.
return false;
}
else if (lower >= upper) // lower == upper NOT useful.
{ // lower >= upper.
*result = policies::raise_domain_error<RealType>(
function,
"lower parameter is %1%, but must be less than upper!", lower, pol);
return false;
}
else
{ // Check lower <= mode <= upper.
if (mode < lower)
{
*result = policies::raise_domain_error<RealType>(
function,
"mode parameter is %1%, but must be >= than lower!", lower, pol);
return false;
}
if (mode > upper)
{
*result = policies::raise_domain_error<RealType>(
function,
"mode parameter is %1%, but must be <= than upper!", upper, pol);
return false;
}
return true; // All OK.
}
} // bool check_triangular
} // namespace detail
template <class RealType = double, class Policy = policies::policy<> >
class triangular_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
: m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
{ // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
// has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
// But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
// where the central value is the most likely and deviations either side equally likely.
RealType result;
detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
}
// Accessor functions.
RealType lower()const
{
return m_lower;
}
RealType mode()const
{
return m_mode;
}
RealType upper()const
{
return m_upper;
}
private:
// Data members:
RealType m_lower; // distribution lower aka a
RealType m_mode; // distribution mode aka c
RealType m_upper; // distribution upper aka b
}; // class triangular_distribution
typedef triangular_distribution<double> triangular;
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
}
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const triangular_distribution<RealType, Policy>& dist)
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
return std::pair<RealType, RealType>(dist.lower(), dist.upper());
}
template <class RealType, class Policy>
RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
{
static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %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;
}
if(false == detail::check_triangular_x(function, x, &result, Policy()))
{
return result;
}
if((x < lower) || (x > upper))
{
return 0;
}
if (x == lower)
{ // (mode - lower) == 0 which would lead to divide by zero!
return (mode == lower) ? 2 / (upper - lower) : RealType(0);
}
else if (x == upper)
{
return (mode == upper) ? 2 / (upper - lower) : RealType(0);
}
else if (x <= mode)
{
return 2 * (x - lower) / ((upper - lower) * (mode - lower));
}
else
{ // (x > mode)
return 2 * (upper - x) / ((upper - lower) * (upper - mode));
}
} // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
template <class RealType, class Policy>
inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
{
static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %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;
}
if(false == detail::check_triangular_x(function, x, &result, Policy()))
{
return result;
}
if((x <= lower))
{
return 0;
}
if (x >= upper)
{
return 1;
}
// else lower < x < upper
if (x <= mode)
{
return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
}
else
{
return 1 - (upper - x) * (upper - x) / ((upper - lower) * (upper - mode));
}
} // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
template <class RealType, class Policy>
RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
{
BOOST_MATH_STD_USING // for ADL of std functions (sqrt).
static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %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;
}
if(false == detail::check_probability(function, p, &result, Policy()))
{
return result;
}
if(p == 0)
{
return lower;
}
if(p == 1)
{
return upper;
}
RealType p0 = (mode - lower) / (upper - lower);
RealType q = 1 - p;
if (p < p0)
{
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 triangular_distribution<RealType, Policy>& dist, const RealType& q)
template <class RealType, class Policy>
RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
{
static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
RealType lower = c.dist.lower();
RealType mode = c.dist.mode();
RealType upper = c.dist.upper();
RealType x = c.param;
RealType result = 0; // of checks.
if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
{
return result;
}
if(false == detail::check_triangular_x(function, x, &result, Policy()))
{
return result;
}
if (x <= lower)
{
return 1;
}
if (x >= upper)
{
return 0;
}
if (x <= mode)
{
return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
}
else
{
return (upper - x) * (upper - x) / ((upper - lower) * (upper - mode));
}
} // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
template <class RealType, class Policy>
RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
{
BOOST_MATH_STD_USING // Aid ADL for sqrt.
static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
RealType l = c.dist.lower();
RealType m = c.dist.mode();
RealType u = c.dist.upper();
RealType q = c.param; // probability 0 to 1.
RealType result = 0; // of checks.
if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
{
return result;
}
if(false == detail::check_probability(function, q, &result, Policy()))
{
return result;
}
if(q == 0)
{
return u;
}
if(q == 1)
{
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