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_GAMMA_HPP
Chris@16: #define BOOST_STATS_GAMMA_HPP
Chris@16: 
Chris@16: // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
Chris@16: // http://mathworld.wolfram.com/GammaDistribution.html
Chris@16: // http://en.wikipedia.org/wiki/Gamma_distribution
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/gamma.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: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool check_gamma_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_gamma_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_gamma(
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_gamma_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 gamma_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    gamma_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_gamma("boost::math::gamma_distribution<%1%>::gamma_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: // NO typedef because of clash with name of gamma function.
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const gamma_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 gamma_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: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_gamma_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(x == 0)
Chris@16:    {
Chris@16:       return 0;
Chris@16:    }
Chris@16:    result = gamma_p_derivative(shape, x / scale, Policy()) / scale;
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_gamma_x(function, x, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = boost::math::gamma_p(shape, x / scale, Policy());
Chris@16:    return result;
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const gamma_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 gamma_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_gamma(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 = gamma_p_inv(shape, p, Policy()) * scale;
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<gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_gamma_x(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = gamma_q(shape, c.param / scale, Policy());
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<gamma_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 gamma_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_gamma(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 = gamma_q_inv(shape, q, Policy()) * scale;
Chris@16: 
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = shape * scale;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const gamma_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::variance(const gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = shape * scale * scale;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const gamma_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::mode(const gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(shape < 1)
Chris@16:       return policies::raise_domain_error<RealType>(
Chris@16:          function,
Chris@16:          "The mode of the gamma distribution is only defined for values of the shape parameter >= 1, but got %1%.",
Chris@16:          shape, Policy());
Chris@16: 
Chris@16:    result = (shape - 1) * scale;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: //template <class RealType, class Policy>
Chris@16: //inline RealType median(const gamma_distribution<RealType, Policy>& dist)
Chris@16: //{  // Rely on default definition in derived accessors.
Chris@16: //}
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = 2 / sqrt(shape);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const gamma_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 gamma_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_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    result = 6 / shape;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const gamma_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_GAMMA_HPP
Chris@16: 
Chris@16: