396 lines
12 KiB
Plaintext
396 lines
12 KiB
Plaintext
// Copyright John Maddock 2006.
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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_WEIBULL_HPP
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#define BOOST_STATS_WEIBULL_HPP
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
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// http://mathworld.wolfram.com/WeibullDistribution.html
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/gamma.hpp>
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#include <boost/math/special_functions/log1p.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 <utility>
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namespace boost{ namespace math
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{
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namespace detail{
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template <class RealType, class Policy>
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inline bool check_weibull_shape(
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const char* function,
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RealType shape,
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RealType* result, const Policy& pol)
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{
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if((shape <= 0) || !(boost::math::isfinite)(shape))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Shape parameter is %1%, but must be > 0 !", shape, 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_weibull_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((x < 0) || !(boost::math::isfinite)(x))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Random variate is %1% but must be >= 0 !", x, 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_weibull(
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const char* function,
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RealType scale,
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RealType shape,
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RealType* result, const Policy& pol)
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{
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return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
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}
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class weibull_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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weibull_distribution(RealType l_shape, RealType l_scale = 1)
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: m_shape(l_shape), m_scale(l_scale)
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{
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RealType result;
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detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
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}
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RealType shape()const
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{
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return m_shape;
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}
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RealType scale()const
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{
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return m_scale;
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}
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private:
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//
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// Data members:
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//
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RealType m_shape; // distribution shape
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RealType m_scale; // distribution scale
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};
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typedef weibull_distribution<double> weibull;
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const weibull_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>(static_cast<RealType>(0), 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 weibull_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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using boost::math::tools::max_value;
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using boost::math::tools::min_value;
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return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
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// A discontinuity at x == 0, so only support down to min_value.
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}
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template <class RealType, class Policy>
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inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_weibull_x(function, x, &result, Policy()))
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return result;
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if(x == 0)
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{
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if(shape == 1)
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{
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return 1 / scale;
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}
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if(shape > 1)
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{
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return 0;
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}
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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}
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result = exp(-pow(x / scale, shape));
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result *= pow(x / scale, shape - 1) * shape / scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_weibull_x(function, x, &result, Policy()))
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return result;
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result = -boost::math::expm1(-pow(x / scale, shape), Policy());
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return result;
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}
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template <class RealType, class Policy>
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inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_probability(function, p, &result, Policy()))
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return result;
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if(p == 1)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
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return result;
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}
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
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RealType shape = c.dist.shape();
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RealType scale = c.dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
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return result;
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result = exp(-pow(c.param / scale, shape));
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return result;
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}
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
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RealType shape = c.dist.shape();
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RealType scale = c.dist.scale();
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RealType q = c.param;
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_probability(function, q, &result, Policy()))
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return result;
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if(q == 0)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = scale * pow(-log(q), 1 / shape);
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return result;
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}
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template <class RealType, class Policy>
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inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
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return result;
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}
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template <class RealType, class Policy>
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inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
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{
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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{
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return result;
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}
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result = boost::math::tgamma(1 + 1 / shape, Policy());
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result *= -result;
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result += boost::math::tgamma(1 + 2 / shape, Policy());
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result *= scale * scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std function pow.
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static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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{
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return result;
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}
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if(shape <= 1)
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return 0;
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result = scale * pow((shape - 1) / shape, 1 / shape);
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return result;
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}
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template <class RealType, class Policy>
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inline RealType median(const weibull_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std function pow.
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static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
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RealType shape = dist.shape(); // Wikipedia k
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RealType scale = dist.scale(); // Wikipedia lambda
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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{
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return result;
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}
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using boost::math::constants::ln_two;
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result = scale * pow(ln_two<RealType>(), 1 / shape);
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return result;
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}
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template <class RealType, class Policy>
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inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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{
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return result;
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}
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RealType g1, g2, g3, d;
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g1 = boost::math::tgamma(1 + 1 / shape, Policy());
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g2 = boost::math::tgamma(1 + 2 / shape, Policy());
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g3 = boost::math::tgamma(1 + 3 / shape, Policy());
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d = pow(g2 - g1 * g1, RealType(1.5));
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result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
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return result;
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RealType g1, g2, g3, g4, d, g1_2, g1_4;
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g1 = boost::math::tgamma(1 + 1 / shape, Policy());
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g2 = boost::math::tgamma(1 + 2 / shape, Policy());
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g3 = boost::math::tgamma(1 + 3 / shape, Policy());
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g4 = boost::math::tgamma(1 + 4 / shape, Policy());
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g1_2 = g1 * g1;
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g1_4 = g1_2 * g1_2;
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d = g2 - g1_2;
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d *= d;
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result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
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result /= d;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
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{
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return kurtosis_excess(dist) + 3;
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}
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} // namespace math
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} // namespace boost
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_STATS_WEIBULL_HPP
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