// Copyright John Maddock 2006, 2007.

// Copyright Paul A. Bristow 2007.



// 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_CHI_SQUARED_HPP

#define BOOST_MATH_DISTRIBUTIONS_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> // complements

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

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



#include <utility>



namespace boost{ namespace math{



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

class chi_squared_distribution

{

public:

   typedef RealType value_type;

   typedef Policy policy_type;



   chi_squared_distribution(RealType i) : m_df(i)

   {

      RealType result;

      detail::check_df(

         "boost::math::chi_squared_distribution<%1%>::chi_squared_distribution", m_df, &result, Policy());

   } // chi_squared_distribution



   RealType degrees_of_freedom()const

   {

      return m_df;

   }



   // Parameter estimation:

   static RealType find_degrees_of_freedom(

      RealType difference_from_variance,

      RealType alpha,

      RealType beta,

      RealType variance,

      RealType hint = 100);



private:

   //

   // Data member:

   //

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

}; // class chi_squared_distribution



typedef chi_squared_distribution<double> chi_squared;



template <class RealType, class Policy>

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

}



template <class RealType, class Policy>

inline const std::pair<RealType, RealType> support(const 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>(0, tools::max_value<RealType>()); // 0 to + infinity.

}



template <class RealType, class Policy>

RealType pdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)

{

   BOOST_MATH_STD_USING  // for ADL of std functions

   RealType degrees_of_freedom = dist.degrees_of_freedom();

   // Error check:

   RealType error_result;



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



   if(false == detail::check_df(

         function, degrees_of_freedom, &error_result, Policy()))

      return error_result;



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

   {

      return policies::raise_domain_error<RealType>(

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

   }



   if(chi_square == 0)

   {

      // Handle special cases:

      if(degrees_of_freedom < 2)

      {

         return policies::raise_overflow_error<RealType>(

            function, 0, Policy());

      }

      else if(degrees_of_freedom == 2)

      {

         return 0.5f;

      }

      else

      {

         return 0;

      }

   }



   return gamma_p_derivative(degrees_of_freedom / 2, chi_square / 2, Policy()) / 2;

} // pdf



template <class RealType, class Policy>

inline RealType cdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)

{

   RealType degrees_of_freedom = dist.degrees_of_freedom();

   // Error check:

   RealType error_result;

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



   if(false == detail::check_df(

         function, degrees_of_freedom, &error_result, Policy()))

      return error_result;



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

   {

      return policies::raise_domain_error<RealType>(

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

   }



   return boost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy());

} // cdf



template <class RealType, class Policy>

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

{

   RealType degrees_of_freedom = dist.degrees_of_freedom();

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(

         function, degrees_of_freedom, &error_result, Policy())

         && detail::check_probability(

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

      return error_result;



   return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy());

} // quantile



template <class RealType, class Policy>

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

{

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

   RealType const& chi_square = c.param;

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(

         function, degrees_of_freedom, &error_result, Policy()))

      return error_result;



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

   {

      return policies::raise_domain_error<RealType>(

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

   }



   return boost::math::gamma_q(degrees_of_freedom / 2, chi_square / 2, Policy());

}



template <class RealType, class Policy>

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

{

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

   RealType const& q = c.param;

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

   // Error check:

   RealType error_result;

   if(false == detail::check_df(

         function, degrees_of_freedom, &error_result, Policy())

         && detail::check_probability(

            function, q, &error_result, Policy()))

      return error_result;



   return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy());

}



template <class RealType, class Policy>

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

{ // Mean of Chi-Squared distribution = v.

  return dist.degrees_of_freedom();

} // mean



template <class RealType, class Policy>

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

{ // Variance of Chi-Squared distribution = 2v.

  return 2 * dist.degrees_of_freedom();

} // variance



template <class RealType, class Policy>

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

{

   RealType df = dist.degrees_of_freedom();

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

   if(df <= 2)

      return policies::raise_domain_error<RealType>(

         function,

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

         df, Policy());

   return df - 2;

}



//template <class RealType, class Policy>

//inline RealType median(const 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 Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",

//         df);

//   return df - RealType(2)/3;

//}

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



template <class RealType, class Policy>

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

{

   BOOST_MATH_STD_USING // For ADL

   RealType df = dist.degrees_of_freedom();

   return sqrt (8 / df);  // == 2 * sqrt(2 / df);

}



template <class RealType, class Policy>

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

{

   RealType df = dist.degrees_of_freedom();

   return 3 + 12 / df;

}



template <class RealType, class Policy>

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

{

   RealType df = dist.degrees_of_freedom();

   return 12 / df;

}



//

// Parameter estimation comes last:

//

namespace detail

{



template <class RealType, class Policy>

struct df_estimator

{

   df_estimator(RealType a, RealType b, RealType variance, RealType delta)

      : alpha(a), beta(b), ratio(delta/variance) {}



   RealType operator()(const RealType& df)

   {

      if(df <= tools::min_value<RealType>())

         return 1;

      chi_squared_distribution<RealType, Policy> cs(df);



      RealType result;

      if(ratio > 0)

      {

         RealType r = 1 + ratio;

         result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;

      }

      else

      {

         RealType r = 1 + ratio;

         result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta;

      }

      return result;

   }

private:

   RealType alpha, beta, ratio;

};



} // namespace detail



template <class RealType, class Policy>

RealType chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom(

   RealType difference_from_variance,

   RealType alpha,

   RealType beta,

   RealType variance,

   RealType hint)

{

   static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";

   // Check for domain errors:

   RealType error_result;

   if(false == detail::check_probability(

         function, alpha, &error_result, Policy())

         && detail::check_probability(function, beta, &error_result, Policy()))

      return error_result;



   if(hint <= 0)

      hint = 1;



   detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);

   tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());

   boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();

   std::pair<RealType, RealType> r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());

   RealType result = r.first + (r.second - r.first) / 2;

   if(max_iter == policies::get_max_root_iterations<Policy>())

   {

      policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"

         " either there is no answer to how many degrees of freedom are required"

         " or the answer is infinite.  Current best guess is %1%", result, Policy());

   }

   return result;

}



} // 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_CHI_SQUARED_HPP

