SV platform dependency builds

// Copyright John Maddock 2010.

// Copyright Paul A. Bristow 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_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP

#define BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP

#include <boost/math/distributions/fwd.hpp>

#include <boost/math/special_functions/gamma.hpp> // for incomplete beta.

#include <boost/math/distributions/complement.hpp> // for complements.

#include <boost/math/distributions/detail/common_error_handling.hpp> // for error checks.

#include <boost/math/special_functions/fpclassify.hpp> // for isfinite

// See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution

// for definitions of this scaled version.

// See http://en.wikipedia.org/wiki/Inverse-chi-square_distribution

// for unscaled version.

// http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html

// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource.

// http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html

#include <utility>

namespace boost{ namespace math{

namespace detail

{

  template <class RealType, class Policy>

  inline bool check_inverse_chi_squared( // Check both distribution parameters.

        const char* function,

        RealType degrees_of_freedom, // degrees_of_freedom (aka nu).

        RealType scale,  // scale (aka sigma^2)

        RealType* result,

        const Policy& pol)

  {

     return check_scale(function, scale, result, pol)

       && check_df(function, degrees_of_freedom,

       result, pol);

  } // bool check_inverse_chi_squared

} // namespace detail

template <class RealType = double, class Policy = policies::policy<> >

class inverse_chi_squared_distribution

{

public:

   typedef RealType value_type;

   typedef Policy policy_type;

   inverse_chi_squared_distribution(RealType df, RealType l_scale) : m_df(df), m_scale (l_scale)

   {

      RealType result;

      detail::check_df(

         "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",

         m_df, &result, Policy())

         && detail::check_scale(

"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",

         m_scale, &result,  Policy());

   } // inverse_chi_squared_distribution constructor 

   inverse_chi_squared_distribution(RealType df = 1) : m_df(df)

   {

      RealType result;

      m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1).

      detail::check_df(

         "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution",

         m_df, &result, Policy());

   } // inverse_chi_squared_distribution

   RealType degrees_of_freedom()const

   {

      return m_df; // aka nu

   }

   RealType scale()const

   {

      return m_scale;  // aka xi

   }

   // Parameter estimation:  NOT implemented yet.

   //static RealType find_degrees_of_freedom(

   //   RealType difference_from_variance,

   //   RealType alpha,

   //   RealType beta,

   //   RealType variance,

   //   RealType hint = 100);

private:

   // Data members:

   RealType m_df;  // degrees of freedom are treated as a real number.

   RealType m_scale;  // distribution scale.

}; // class chi_squared_distribution

typedef inverse_chi_squared_distribution<double> inverse_chi_squared;

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> range(const inverse_chi_squared_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>()); // 0 to + infinity.

}

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> support(const inverse_chi_squared_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.

   return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.

}

template <class RealType, class Policy>

RealType pdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)

{

   BOOST_MATH_STD_USING  // for ADL of std functions.

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

   RealType error_result;

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

   if(false == detail::check_inverse_chi_squared

     (function, df, scale, &error_result, Policy())

     )

   { // Bad distribution.

      return error_result;

   }

   if((x < 0) || !(boost::math::isfinite)(x))

   { // Bad x.

      return policies::raise_domain_error<RealType>(

         function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());

   }

   if(x == 0)

   { // Treat as special case.

     return 0;

   }

   // Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2) 

   // so use inverse gamma pdf with shape = df/2, scale df * scale /2 

   // RealType shape = df /2; // inv_gamma shape

   // RealType scale = df * scale/2; // inv_gamma scale

   // RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x);

   RealType result = df * scale/2 / x;

   if(result < tools::min_value<RealType>())

      return 0; // Random variable is near enough infinite.

   result = gamma_p_derivative(df/2, result, Policy()) * df * scale/2;

   if(result != 0) // prevent 0 / 0,  gamma_p_derivative -> 0 faster than x^2

      result /= (x * x);

   return result;

} // pdf

template <class RealType, class Policy>

inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)

{

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

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

   RealType error_result;

   if(false ==

       detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy())

     )

   { // Bad distribution.

      return error_result;

   }

   if((x < 0) || !(boost::math::isfinite)(x))

   { // Bad x.

      return policies::raise_domain_error<RealType>(

         function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());

   }

   if (x == 0)

   { // Treat zero as a special case.

     return 0;

   }

   // RealType shape = df /2; // inv_gamma shape,

   // RealType scale = df * scale/2; // inv_gamma scale,

   // result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code.

   return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy());

} // cdf

template <class RealType, class Policy>

inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p)

{

   using boost::math::gamma_q_inv;

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(

         function, df, &error_result, Policy())

         && detail::check_probability(

            function, p, &error_result, Policy()))

   {

      return error_result;

   }

   if(false == detail::check_probability(

            function, p, &error_result, Policy()))

   {

      return error_result;

   }

   // RealType shape = df /2; // inv_gamma shape,

   // RealType scale = df * scale/2; // inv_gamma scale,

   // result = scale / gamma_q_inv(shape, p, Policy());

      RealType result = gamma_q_inv(df /2, p, Policy());

      if(result == 0)

         return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy());

      result = df * (scale / 2) / result;

      return result;

} // quantile

template <class RealType, class Policy>

inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)

{

   using boost::math::gamma_q_inv;

   RealType const& df = c.dist.degrees_of_freedom();

   RealType const& scale = c.dist.scale();

   RealType const& x = c.param;

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(

         function, df, &error_result, Policy()))

   {

      return error_result;

   }

   if (x == 0)

   { // Treat zero as a special case.

     return 1;

   }

   if((x < 0) || !(boost::math::isfinite)(x))

   {

      return policies::raise_domain_error<RealType>(

         function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy());

   }

   // RealType shape = df /2; // inv_gamma shape,

   // RealType scale = df * scale/2; // inv_gamma scale,

   // result = gamma_p(shape, scale/c.param, Policy()); use inv_gamma.

   return gamma_p(df / 2, (df * scale/2) / x, Policy()); // OK

} // cdf(complemented

template <class RealType, class Policy>

inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)

{

   using boost::math::gamma_q_inv;

   RealType const& df = c.dist.degrees_of_freedom();

   RealType const& scale = c.dist.scale();

   RealType const& q = c.param;

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(function, df, &error_result, Policy()))

   {

      return error_result;

   }

   if(false == detail::check_probability(function, q, &error_result, Policy()))

   {

      return error_result;

   }

   // RealType shape = df /2; // inv_gamma shape,

   // RealType scale = df * scale/2; // inv_gamma scale,

   // result = scale / gamma_p_inv(shape, q, Policy());  // using inv_gamma.

   RealType result = gamma_p_inv(df/2, q, Policy());

   if(result == 0)

      return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy());

   result = (df * scale / 2) / result;

   return result;

} // quantile(const complement

template <class RealType, class Policy>

inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{ // Mean of inverse Chi-Squared distribution.

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

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

   if(df <= 2)

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a mode for degrees of freedom > 2, but got degrees of freedom = %1%.",

         df, Policy());

  return (df * scale) / (df - 2);

} // mean

template <class RealType, class Policy>

inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{ // Variance of inverse Chi-Squared distribution.

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

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

   if(df <= 4)

   {

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.",

         df, Policy());

   }

   return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4));

} // variance

template <class RealType, class Policy>

inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{ // mode is not defined in Mathematica.

  // See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution

  // for origin of the formula used below.

   RealType df = dist.degrees_of_freedom();

   RealType scale = dist.scale();

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

   if(df < 0)

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",

         df, Policy());

   return (df * scale) / (df + 2);

}

//template <class RealType, class Policy>

//inline RealType median(const inverse_chi_squared_distribution<RealType, Policy>& dist)

//{ // Median is given by Quantile[dist, 1/2]

//   RealType df = dist.degrees_of_freedom();

//   if(df <= 1)

//      return tools::domain_error<RealType>(

//         BOOST_CURRENT_FUNCTION,

//         "The inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.",

//         df);

//   return df;

//}

// Now implemented via quantile(half) in derived accessors.

template <class RealType, class Policy>

inline RealType skewness(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{

   BOOST_MATH_STD_USING // For ADL

   RealType df = dist.degrees_of_freedom();

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

   if(df <= 6)

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.",

         df, Policy());

   return 4 * sqrt (2 * (df - 4)) / (df - 6);  // Not a function of scale.

}

template <class RealType, class Policy>

inline RealType kurtosis(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{

   RealType df = dist.degrees_of_freedom();

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

   if(df <= 8)

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.",

         df, Policy());

   return kurtosis_excess(dist) + 3;

}

template <class RealType, class Policy>

inline RealType kurtosis_excess(const inverse_chi_squared_distribution<RealType, Policy>& dist)

{

   RealType df = dist.degrees_of_freedom();

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

   if(df <= 8)

      return policies::raise_domain_error<RealType>(

         function,

         "inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.",

         df, Policy());

   return 12 * (5 * df - 22) / ((df - 6 )*(df - 8));  // Not a function of scale.

}

//

// Parameter estimation comes last:

//

} // 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_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP