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