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/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/inverse_gamma.hpp (15389B)

// inverse_gamma.hpp

//  Copyright Paul A. Bristow 2010.
//  Copyright John Maddock 2010.
//  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_INVERSE_GAMMA_HPP
#define BOOST_STATS_INVERSE_GAMMA_HPP

// Inverse Gamma Distribution is a two-parameter family
// of continuous probability distributions
// on the positive real line, which is the distribution of
// the reciprocal of a variable distributed according to the gamma distribution.

// http://en.wikipedia.org/wiki/Inverse-gamma_distribution
// http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html

// See also gamma distribution at gamma.hpp:
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
// http://mathworld.wolfram.com/GammaDistribution.html
// http://en.wikipedia.org/wiki/Gamma_distribution

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/gamma.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_inverse_gamma_shape(
      const char* function, // inverse_gamma
      RealType shape, // shape aka alpha
      RealType* result, // to update, perhaps with NaN
      const Policy& pol)
{  // Sources say shape argument must be > 0
   // but seems logical to allow shape zero as special case,
   // returning pdf and cdf zero (but not < 0).
   // (Functions like mean, variance with other limits on shape are checked
   // in version including an operator & limit below).
   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;
} //bool check_inverse_gamma_shape

template <class RealType, class Policy>
inline bool check_inverse_gamma_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_inverse_gamma(
      const char* function, // TODO swap these over, so shape is first.
      RealType scale,  // scale aka beta
      RealType shape, // shape aka alpha
      RealType* result, const Policy& pol)
{
   return check_scale(function, scale, result, pol)
     && check_inverse_gamma_shape(function, shape, result, pol);
} // bool check_inverse_gamma

} // namespace detail

template <class RealType = double, class Policy = policies::policy<> >
class inverse_gamma_distribution
{
public:
   typedef RealType value_type;
   typedef Policy policy_type;

inverse_gamma_distribution(RealType l_shape = 1, RealType l_scale = 1)
      : m_shape(l_shape), m_scale(l_scale)
   {
      RealType result;
      detail::check_inverse_gamma(
        "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_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 inverse_gamma_distribution<double> inverse_gamma;
// typedef - but potential clash with name of inverse gamma *function*.
// but there is a typedef for gamma
//   typedef boost::math::gamma_distribution<Type, Policy> gamma;

// Allow random variable x to be zero, treated as a special case (unlike some definitions).

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const inverse_gamma_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 inverse_gamma_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>(static_cast<RealType>(0),  max_value<RealType>());
}

template <class RealType, class Policy>
inline RealType pdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::pdf(const inverse_gamma_distribution<%1%>&, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
   { // distribution parameters bad.
      return result;
   } 
   if(x == 0)
   { // Treat random variate zero as a special case.
      return 0;
   }
   else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
   { // x bad.
      return result;
   }
   result = scale / x;
   if(result < tools::min_value<RealType>())
      return 0;  // random variable is infinite or so close as to make no difference.
   result = gamma_p_derivative(shape, result, Policy()) * scale;
   if(0 != result)
   {
      if(x < 0)
      {
         // x * x may under or overflow, likewise our result,
         // so be extra careful about the arithmetic:
         RealType lim = tools::max_value<RealType>() * x;
         if(lim < result)
            return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
         result /= x;
         if(lim < result)
            return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
         result /= x;
      }
      result /= (x * x);
   }
   // better than naive
   // result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape);
   return result;
} // pdf

template <class RealType, class Policy>
inline RealType cdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::cdf(const inverse_gamma_distribution<%1%>&, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

template <class RealType, class Policy>
inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p)
{
   BOOST_MATH_STD_USING  // for ADL of std functions
   using boost::math::gamma_q_inv;

static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_inverse_gamma(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 = gamma_q_inv(shape, p, Policy());
   if((result < 1) && (result * tools::max_value<RealType>() < scale))
      return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
   result = scale / result;
   return result;
}

template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";

RealType shape = c.dist.shape();
   RealType scale = c.dist.scale();

RealType result = 0;
   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
      return result;
   if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy()))
      return result;

if(c.param == 0)
      return 1; // Avoid division by zero

//result = 1. - gamma_q(shape, c.param / scale, Policy());
   result = gamma_p(shape, scale/c.param, Policy());
   return result;
}

template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";

RealType shape = c.dist.shape();
   RealType scale = c.dist.scale();
   RealType q = c.param;

if(q == 0)
   {
      return policies::raise_overflow_error<RealType>(function, 0, Policy());
   }
   result = gamma_p_inv(shape, q, Policy());
   if((result < 1) && (result * tools::max_value<RealType>() < scale))
      return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
   result = scale / result;
   return result;
}

template <class RealType, class Policy>
inline RealType mean(const inverse_gamma_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::mean(const inverse_gamma_distribution<%1%>&)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;

if(false == detail::check_scale(function, scale, &result, Policy()))
   {
     return result;
   }
   if((shape <= 1) || !(boost::math::isfinite)(shape))
   {
     result = policies::raise_domain_error<RealType>(
       function,
       "Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy());
     return result;
   }
  result = scale / (shape - 1);
  return result;
} // mean

template <class RealType, class Policy>
inline RealType variance(const inverse_gamma_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::variance(const inverse_gamma_distribution<%1%>&)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
      if(false == detail::check_scale(function, scale, &result, Policy()))
   {
     return result;
   }
   if((shape <= 2) || !(boost::math::isfinite)(shape))
   {
     result = policies::raise_domain_error<RealType>(
       function,
       "Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy());
     return result;
   }
   result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2));
   return result;
}

template <class RealType, class Policy>
inline RealType mode(const inverse_gamma_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::mode(const inverse_gamma_distribution<%1%>&)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
   {
      return result;
   }
   // Only defined for shape >= 0, but is checked by check_inverse_gamma.
   result = scale / (shape + 1);
   return result;
}

//template <class RealType, class Policy>
//inline RealType median(const gamma_distribution<RealType, Policy>& dist)
//{  // Wikipedia does not define median,
     // so rely on default definition quantile(0.5) in derived accessors.
//  return result.
//}

template <class RealType, class Policy>
inline RealType skewness(const inverse_gamma_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::skewness(const inverse_gamma_distribution<%1%>&)";

RealType shape = dist.shape();
   RealType scale = dist.scale();
   RealType result = 0;

if(false == detail::check_scale(function, scale, &result, Policy()))
   {
     return result;
   }
   if((shape <= 3) || !(boost::math::isfinite)(shape))
   {
     result = policies::raise_domain_error<RealType>(
       function,
       "Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy());
     return result;
   }
   result = (4 * sqrt(shape - 2) ) / (shape - 3);
   return result;
}

template <class RealType, class Policy>
inline RealType kurtosis_excess(const inverse_gamma_distribution<RealType, Policy>& dist)
{
   BOOST_MATH_STD_USING  // for ADL of std functions

static const char* function = "boost::math::kurtosis_excess(const inverse_gamma_distribution<%1%>&)";

RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;
   if(false == detail::check_scale(function, scale, &result, Policy()))
   {
     return result;
   }
   if((shape <= 4) || !(boost::math::isfinite)(shape))
   {
     result = policies::raise_domain_error<RealType>(
       function,
       "Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy());
     return result;
   }
   result = (30 * shape - 66) / ((shape - 3) * (shape - 4));
   return result;
}

template <class RealType, class Policy>
inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist)
{
  static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)";
   RealType shape = dist.shape();
   RealType scale = dist.scale();

RealType result = 0;

if(false == detail::check_scale(function, scale, &result, Policy()))
   {
     return result;
   }
   if((shape <= 4) || !(boost::math::isfinite)(shape))
   {
     result = policies::raise_domain_error<RealType>(
       function,
       "Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy());
     return result;
   }
  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_INVERSE_GAMMA_HPP

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