Chris@16: //  Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_WEIBULL_HPP
Chris@16: #define BOOST_STATS_WEIBULL_HPP
Chris@16: 
Chris@16: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
Chris@16: // http://mathworld.wolfram.com/WeibullDistribution.html
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/gamma.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math
Chris@16: {
Chris@16: namespace detail{
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool check_weibull_shape(
Chris@16:       const char* function,
Chris@16:       RealType shape,
Chris@16:       RealType* result, const Policy& pol)
Chris@16: {
Chris@16:    if((shape <= 0) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:       *result = policies::raise_domain_error<RealType>(
Chris@16:          function,
Chris@16:          "Shape parameter is %1%, but must be > 0 !", shape, pol);
Chris@16:       return false;
Chris@16:    }
Chris@16:    return true;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool check_weibull_x(
Chris@16:       const char* function,
Chris@16:       RealType const& x,
Chris@16:       RealType* result, const Policy& pol)
Chris@16: {
Chris@16:    if((x < 0) || !(boost::math::isfinite)(x))
Chris@16:    {
Chris@16:       *result = policies::raise_domain_error<RealType>(
Chris@16:          function,
Chris@16:          "Random variate is %1% but must be >= 0 !", x, pol);
Chris@16:       return false;
Chris@16:    }
Chris@16:    return true;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool check_weibull(
Chris@16:       const char* function,
Chris@16:       RealType scale,
Chris@16:       RealType shape,
Chris@16:       RealType* result, const Policy& pol)
Chris@16: {
Chris@16:    return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class weibull_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    weibull_distribution(RealType l_shape, RealType l_scale = 1)
Chris@16:       : m_shape(l_shape), m_scale(l_scale)
Chris@16:    {
Chris@16:       RealType result;
Chris@16:       detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    RealType shape()const
Chris@16:    {
Chris@16:       return m_shape;
Chris@16:    }
Chris@16: 
Chris@16:    RealType scale()const
Chris@16:    {
Chris@16:       return m_scale;
Chris@16:    }
Chris@16: private:
Chris@16:    //
Chris@16:    // Data members:
Chris@16:    //
Chris@16:    RealType m_shape;     // distribution shape
Chris@16:    RealType m_scale;     // distribution scale
Chris@16: };
Chris@16: 
Chris@16: typedef weibull_distribution<double> weibull;
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of permissible values for random variable x.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of supported values for random variable x.
Chris@16:    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:    using boost::math::tools::max_value;
Chris@16:    using boost::math::tools::min_value;
Chris@16:    return std::pair<RealType, RealType>(min_value<RealType>(),  max_value<RealType>());
Chris@16:    // A discontinuity at x == 0, so only support down to min_value.
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_weibull_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(x == 0)
Chris@16:    {
Chris@16:       if(shape == 1)
Chris@16:       {
Chris@16:          return 1 / scale;
Chris@16:       }
Chris@16:       if(shape > 1)
Chris@16:       {
Chris@16:          return 0;
Chris@16:       }
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    result = exp(-pow(x / scale, shape));
Chris@16:    result *= pow(x / scale, shape - 1) * shape / scale;
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_weibull_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = -boost::math::expm1(-pow(x / scale, shape), Policy());
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_probability(function, p, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(p == 1)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
Chris@16: 
Chris@16:    RealType shape = c.dist.shape();
Chris@16:    RealType scale = c.dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = exp(-pow(c.param / scale, shape));
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
Chris@16: 
Chris@16:    RealType shape = c.dist.shape();
Chris@16:    RealType scale = c.dist.scale();
Chris@16:    RealType q = c.param;
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_probability(function, q, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(q == 0)
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16: 
Chris@16:    result = scale * pow(-log(q), 1 / shape);
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    result = boost::math::tgamma(1 + 1 / shape, Policy());
Chris@16:    result *= -result;
Chris@16:    result += boost::math::tgamma(1 + 2 / shape, Policy());
Chris@16:    result *= scale * scale;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std function pow.
Chris@16: 
Chris@16:    static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(shape <= 1)
Chris@16:       return 0;
Chris@16:    result = scale * pow((shape - 1) / shape, 1 / shape);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std function pow.
Chris@16: 
Chris@16:    static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType shape = dist.shape(); // Wikipedia k
Chris@16:    RealType scale = dist.scale(); // Wikipedia lambda
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    using boost::math::constants::ln_two;
Chris@16:    result = scale * pow(ln_two<RealType>(), 1 / shape);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    RealType g1, g2, g3, d;
Chris@16: 
Chris@16:    g1 = boost::math::tgamma(1 + 1 / shape, Policy());
Chris@16:    g2 = boost::math::tgamma(1 + 2 / shape, Policy());
Chris@16:    g3 = boost::math::tgamma(1 + 3 / shape, Policy());
Chris@16:    d = pow(g2 - g1 * g1, RealType(1.5));
Chris@16: 
Chris@16:    result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16: 
Chris@16:    static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    RealType g1, g2, g3, g4, d, g1_2, g1_4;
Chris@16: 
Chris@16:    g1 = boost::math::tgamma(1 + 1 / shape, Policy());
Chris@16:    g2 = boost::math::tgamma(1 + 2 / shape, Policy());
Chris@16:    g3 = boost::math::tgamma(1 + 3 / shape, Policy());
Chris@16:    g4 = boost::math::tgamma(1 + 4 / shape, Policy());
Chris@16:    g1_2 = g1 * g1;
Chris@16:    g1_4 = g1_2 * g1_2;
Chris@16:    d = g2 - g1_2;
Chris@16:    d *= d;
Chris@16: 
Chris@16:    result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
Chris@16:    result /= d;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return kurtosis_excess(dist) + 3;
Chris@16: }
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_WEIBULL_HPP
Chris@16: 
Chris@16: