Chris@16: // inverse_gamma.hpp
Chris@16: 
Chris@16: //  Copyright Paul A. Bristow 2010.
Chris@16: //  Copyright John Maddock 2010.
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_INVERSE_GAMMA_HPP
Chris@16: #define BOOST_STATS_INVERSE_GAMMA_HPP
Chris@16: 
Chris@16: // Inverse Gamma Distribution is a two-parameter family
Chris@16: // of continuous probability distributions
Chris@16: // on the positive real line, which is the distribution of
Chris@16: // the reciprocal of a variable distributed according to the gamma distribution.
Chris@16: 
Chris@16: // http://en.wikipedia.org/wiki/Inverse-gamma_distribution
Chris@16: // http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html
Chris@16: 
Chris@16: // See also gamma distribution at gamma.hpp:
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_inverse_gamma_shape(
Chris@16:       const char* function, // inverse_gamma
Chris@16:       RealType shape, // shape aka alpha
Chris@16:       RealType* result, // to update, perhaps with NaN
Chris@16:       const Policy& pol)
Chris@16: {  // Sources say shape argument must be > 0
Chris@16:    // but seems logical to allow shape zero as special case,
Chris@16:    // returning pdf and cdf zero (but not < 0).
Chris@16:    // (Functions like mean, variance with other limits on shape are checked
Chris@16:    // in version including an operator & limit below).
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: } //bool check_inverse_gamma_shape
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline bool check_inverse_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_inverse_gamma(
Chris@16:       const char* function, // TODO swap these over, so shape is first.
Chris@16:       RealType scale,  // scale aka beta
Chris@16:       RealType shape, // shape aka alpha
Chris@16:       RealType* result, const Policy& pol)
Chris@16: {
Chris@16:    return check_scale(function, scale, result, pol)
Chris@16:      && check_inverse_gamma_shape(function, shape, result, pol);
Chris@16: } // bool check_inverse_gamma
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class inverse_gamma_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    inverse_gamma_distribution(RealType l_shape = 1, RealType l_scale = 1)
Chris@16:       : m_shape(l_shape), m_scale(l_scale)
Chris@16:    {
Chris@16:       RealType result;
Chris@16:       detail::check_inverse_gamma(
Chris@16:         "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_distribution",
Chris@16:         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 inverse_gamma_distribution<double> inverse_gamma;
Chris@16: // typedef - but potential clash with name of inverse gamma *function*.
Chris@16: // but there is a typedef for gamma
Chris@16: //   typedef boost::math::gamma_distribution<Type, Policy> gamma;
Chris@16: 
Chris@16: // Allow random variable x to be zero, treated as a special case (unlike some definitions).
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const inverse_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 inverse_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>(static_cast<RealType>(0),  max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const inverse_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 inverse_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_inverse_gamma(function, scale, shape, &result, Policy()))
Chris@16:    { // distribution parameters bad.
Chris@16:       return result;
Chris@16:    } 
Chris@16:    if(x == 0)
Chris@16:    { // Treat random variate zero as a special case.
Chris@16:       return 0;
Chris@16:    }
Chris@16:    else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
Chris@16:    { // x bad.
Chris@16:       return result;
Chris@16:    }
Chris@16:    result = scale / x;
Chris@16:    if(result < tools::min_value<RealType>())
Chris@16:       return 0;  // random variable is infinite or so close as to make no difference.
Chris@16:    result = gamma_p_derivative(shape, result, Policy()) * scale;
Chris@16:    if(0 != result)
Chris@16:    {
Chris@16:       if(x < 0)
Chris@16:       {
Chris@16:          // x * x may under or overflow, likewise our result,
Chris@16:          // so be extra careful about the arithmetic:
Chris@16:          RealType lim = tools::max_value<RealType>() * x;
Chris@16:          if(lim < result)
Chris@16:             return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
Chris@16:          result /= x;
Chris@16:          if(lim < result)
Chris@16:             return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
Chris@16:          result /= x;
Chris@16:       }
Chris@16:       result /= (x * x);
Chris@16:    }
Chris@16:    // better than naive
Chris@16:    // result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape);
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const inverse_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 inverse_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_inverse_gamma(function, scale, shape, &result, Policy()))
Chris@16:    { // distribution parameters bad.
Chris@16:       return result;
Chris@16:    }
Chris@16:    if (x == 0)
Chris@16:    { // Treat zero as a special case.
Chris@16:      return 0;
Chris@16:    }
Chris@16:    else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
Chris@16:    { // x bad
Chris@16:       return result;
Chris@16:    }
Chris@16:    result = boost::math::gamma_q(shape, scale / x, Policy());
Chris@16:    // result = tgamma(shape, scale / x) / tgamma(shape); // naive using tgamma
Chris@16:    return result;
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16:    using boost::math::gamma_q_inv;
Chris@16: 
Chris@16:    static const char* function = "boost::math::quantile(const inverse_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_inverse_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:    if(p == 1)
Chris@16:    {
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    result = gamma_q_inv(shape, p, Policy());
Chris@16:    if((result < 1) && (result * tools::max_value<RealType>() < scale))
Chris@16:       return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
Chris@16:    result = scale / result;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<inverse_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_inverse_gamma(function, scale, shape, &result, Policy()))
Chris@16:       return result;
Chris@16:    if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy()))
Chris@16:       return result;
Chris@16: 
Chris@16:    if(c.param == 0)
Chris@16:       return 1; // Avoid division by zero
Chris@16: 
Chris@16:    //result = 1. - gamma_q(shape, c.param / scale, Policy());
Chris@16:    result = gamma_p(shape, scale/c.param, Policy());
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<inverse_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 inverse_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_inverse_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:    {
Chris@16:       return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    result = gamma_p_inv(shape, q, Policy());
Chris@16:    if((result < 1) && (result * tools::max_value<RealType>() < scale))
Chris@16:       return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
Chris@16:    result = scale / result;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const inverse_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 inverse_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: 
Chris@16:    if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if((shape <= 1) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:      result = policies::raise_domain_error<RealType>(
Chris@16:        function,
Chris@16:        "Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy());
Chris@16:      return result;
Chris@16:    }
Chris@16:   result = scale / (shape - 1);
Chris@16:   return result;
Chris@16: } // mean
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const inverse_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 inverse_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_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if((shape <= 2) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:      result = policies::raise_domain_error<RealType>(
Chris@16:        function,
Chris@16:        "Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy());
Chris@16:      return result;
Chris@16:    }
Chris@16:    result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2));
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const inverse_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 inverse_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_inverse_gamma(function, scale, shape, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    // Only defined for shape >= 0, but is checked by check_inverse_gamma.
Chris@16:    result = scale / (shape + 1);
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: //{  // Wikipedia does not define median,
Chris@16:      // so rely on default definition quantile(0.5) in derived accessors.
Chris@16: //  return result.
Chris@16: //}
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const inverse_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 inverse_gamma_distribution<%1%>&)";
Chris@16: 
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16:    RealType result = 0;
Chris@16: 
Chris@16:    if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if((shape <= 3) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:      result = policies::raise_domain_error<RealType>(
Chris@16:        function,
Chris@16:        "Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy());
Chris@16:      return result;
Chris@16:    }
Chris@16:    result = (4 * sqrt(shape - 2) ) / (shape - 3);
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const inverse_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 inverse_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_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if((shape <= 4) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:      result = policies::raise_domain_error<RealType>(
Chris@16:        function,
Chris@16:        "Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy());
Chris@16:      return result;
Chris@16:    }
Chris@16:    result = (30 * shape - 66) / ((shape - 3) * (shape - 4));
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:   static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)";
Chris@16:    RealType shape = dist.shape();
Chris@16:    RealType scale = dist.scale();
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16: 
Chris@16:   if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:    {
Chris@16:      return result;
Chris@16:    }
Chris@16:    if((shape <= 4) || !(boost::math::isfinite)(shape))
Chris@16:    {
Chris@16:      result = policies::raise_domain_error<RealType>(
Chris@16:        function,
Chris@16:        "Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy());
Chris@16:      return result;
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_INVERSE_GAMMA_HPP