Chris@16: // Copyright John Maddock 2006, 2007.
Chris@16: // Copyright Paul A. Bristow 2008, 2010.
Chris@16: 
Chris@16: // Use, modification and distribution are subject to the
Chris@16: // Boost Software License, Version 1.0.
Chris@16: // (See accompanying file LICENSE_1_0.txt
Chris@16: // or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
Chris@16: #define BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/gamma.hpp> // for incomplete beta.
Chris@16: #include <boost/math/distributions/complement.hpp> // complements
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
Chris@16: #include <boost/math/special_functions/fpclassify.hpp>
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class chi_squared_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    chi_squared_distribution(RealType i) : m_df(i)
Chris@16:    {
Chris@16:       RealType result;
Chris@16:       detail::check_df(
Chris@16:          "boost::math::chi_squared_distribution<%1%>::chi_squared_distribution", m_df, &result, Policy());
Chris@16:    } // chi_squared_distribution
Chris@16: 
Chris@16:    RealType degrees_of_freedom()const
Chris@16:    {
Chris@16:       return m_df;
Chris@16:    }
Chris@16: 
Chris@16:    // Parameter estimation:
Chris@16:    static RealType find_degrees_of_freedom(
Chris@16:       RealType difference_from_variance,
Chris@16:       RealType alpha,
Chris@16:       RealType beta,
Chris@16:       RealType variance,
Chris@16:       RealType hint = 100);
Chris@16: 
Chris@16: private:
Chris@16:    //
Chris@16:    // Data member:
Chris@16:    //
Chris@16:    RealType m_df; // degrees of freedom is a positive real number.
Chris@16: }; // class chi_squared_distribution
Chris@16: 
Chris@16: typedef chi_squared_distribution<double> chi_squared;
Chris@16: 
Chris@101: #ifdef BOOST_MSVC
Chris@101: #pragma warning(push)
Chris@101: #pragma warning(disable:4127)
Chris@101: #endif
Chris@101: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const chi_squared_distribution<RealType, Policy>& /*dist*/)
Chris@16: { // Range of permissible values for random variable x.
Chris@16:   if (std::numeric_limits<RealType>::has_infinity)
Chris@16:   { 
Chris@16:     return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity.
Chris@16:   }
Chris@16:   else
Chris@16:   {
Chris@16:     using boost::math::tools::max_value;
Chris@16:     return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max.
Chris@16:   }
Chris@16: }
Chris@16: 
Chris@101: #ifdef BOOST_MSVC
Chris@101: #pragma warning(pop)
Chris@101: #endif
Chris@101: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> support(const chi_squared_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:    return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType pdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING  // for ADL of std functions
Chris@16:    RealType degrees_of_freedom = dist.degrees_of_freedom();
Chris@16:    // Error check:
Chris@16:    RealType error_result;
Chris@16: 
Chris@16:    static const char* function = "boost::math::pdf(const chi_squared_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    if(false == detail::check_df(
Chris@16:          function, degrees_of_freedom, &error_result, Policy()))
Chris@16:       return error_result;
Chris@16: 
Chris@16:    if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
Chris@16:    {
Chris@16:       return policies::raise_domain_error<RealType>(
Chris@16:          function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    if(chi_square == 0)
Chris@16:    {
Chris@16:       // Handle special cases:
Chris@16:       if(degrees_of_freedom < 2)
Chris@16:       {
Chris@16:          return policies::raise_overflow_error<RealType>(
Chris@16:             function, 0, Policy());
Chris@16:       }
Chris@16:       else if(degrees_of_freedom == 2)
Chris@16:       {
Chris@16:          return 0.5f;
Chris@16:       }
Chris@16:       else
Chris@16:       {
Chris@16:          return 0;
Chris@16:       }
Chris@16:    }
Chris@16: 
Chris@16:    return gamma_p_derivative(degrees_of_freedom / 2, chi_square / 2, Policy()) / 2;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
Chris@16: {
Chris@16:    RealType degrees_of_freedom = dist.degrees_of_freedom();
Chris@16:    // Error check:
Chris@16:    RealType error_result;
Chris@16:    static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:    if(false == detail::check_df(
Chris@16:          function, degrees_of_freedom, &error_result, Policy()))
Chris@16:       return error_result;
Chris@16: 
Chris@16:    if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
Chris@16:    {
Chris@16:       return policies::raise_domain_error<RealType>(
Chris@16:          function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    return boost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy());
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const chi_squared_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    RealType degrees_of_freedom = dist.degrees_of_freedom();
Chris@16:    static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
Chris@16:    // Error check:
Chris@16:    RealType error_result;
Chris@16:    if(false ==
Chris@16:      (
Chris@16:        detail::check_df(function, degrees_of_freedom, &error_result, Policy())
Chris@16:        && detail::check_probability(function, p, &error_result, Policy()))
Chris@16:      )
Chris@16:      return error_result;
Chris@16: 
Chris@16:    return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy());
Chris@16: } // quantile
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
Chris@16:    RealType const& chi_square = c.param;
Chris@16:    static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
Chris@16:    // Error check:
Chris@16:    RealType error_result;
Chris@16:    if(false == detail::check_df(
Chris@16:          function, degrees_of_freedom, &error_result, Policy()))
Chris@16:       return error_result;
Chris@16: 
Chris@16:    if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
Chris@16:    {
Chris@16:       return policies::raise_domain_error<RealType>(
Chris@16:          function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
Chris@16:    }
Chris@16: 
Chris@16:    return boost::math::gamma_q(degrees_of_freedom / 2, chi_square / 2, Policy());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
Chris@16:    RealType const& q = c.param;
Chris@16:    static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
Chris@16:    // Error check:
Chris@16:    RealType error_result;
Chris@16:    if(false == (
Chris@16:      detail::check_df(function, degrees_of_freedom, &error_result, Policy())
Chris@16:      && detail::check_probability(function, q, &error_result, Policy()))
Chris@16:      )
Chris@16:     return error_result;
Chris@16: 
Chris@16:    return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: { // Mean of Chi-Squared distribution = v.
Chris@16:   return dist.degrees_of_freedom();
Chris@16: } // mean
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: { // Variance of Chi-Squared distribution = 2v.
Chris@16:   return 2 * dist.degrees_of_freedom();
Chris@16: } // variance
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType df = dist.degrees_of_freedom();
Chris@16:    static const char* function = "boost::math::mode(const chi_squared_distribution<%1%>&)";
Chris@16:    // Most sources only define mode for df >= 2,
Chris@16:    // but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0;
Chris@16:    // So one could extend the definition of mode thus:
Chris@16:    //if(df < 0)
Chris@16:    //{
Chris@16:    //   return policies::raise_domain_error<RealType>(
Chris@16:    //      function,
Chris@16:    //      "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
Chris@16:    //      df, Policy());
Chris@16:    //}
Chris@16:    //return (df <= 2) ? 0 : df - 2;
Chris@16: 
Chris@16:    if(df < 2)
Chris@16:       return policies::raise_domain_error<RealType>(
Chris@16:          function,
Chris@16:          "Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
Chris@16:          df, Policy());
Chris@16:    return df - 2;
Chris@16: }
Chris@16: 
Chris@16: //template <class RealType, class Policy>
Chris@16: //inline RealType median(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: //{ // Median is given by Quantile[dist, 1/2]
Chris@16: //   RealType df = dist.degrees_of_freedom();
Chris@16: //   if(df <= 1)
Chris@16: //      return tools::domain_error<RealType>(
Chris@16: //         BOOST_CURRENT_FUNCTION,
Chris@16: //         "The Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
Chris@16: //         df);
Chris@16: //   return df - RealType(2)/3;
Chris@16: //}
Chris@16: // Now implemented via quantile(half) in derived accessors.
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // For ADL
Chris@16:    RealType df = dist.degrees_of_freedom();
Chris@16:    return sqrt (8 / df);  // == 2 * sqrt(2 / df);
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType df = dist.degrees_of_freedom();
Chris@16:    return 3 + 12 / df;
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const chi_squared_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType df = dist.degrees_of_freedom();
Chris@16:    return 12 / df;
Chris@16: }
Chris@16: 
Chris@16: //
Chris@16: // Parameter estimation comes last:
Chris@16: //
Chris@16: namespace detail
Chris@16: {
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: struct df_estimator
Chris@16: {
Chris@16:    df_estimator(RealType a, RealType b, RealType variance, RealType delta)
Chris@16:       : alpha(a), beta(b), ratio(delta/variance)
Chris@16:    { // Constructor
Chris@16:    }
Chris@16: 
Chris@16:    RealType operator()(const RealType& df)
Chris@16:    {
Chris@16:       if(df <= tools::min_value<RealType>())
Chris@16:          return 1;
Chris@16:       chi_squared_distribution<RealType, Policy> cs(df);
Chris@16: 
Chris@16:       RealType result;
Chris@16:       if(ratio > 0)
Chris@16:       {
Chris@16:          RealType r = 1 + ratio;
Chris@16:          result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;
Chris@16:       }
Chris@16:       else
Chris@16:       { // ratio <= 0
Chris@16:          RealType r = 1 + ratio;
Chris@16:          result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta;
Chris@16:       }
Chris@16:       return result;
Chris@16:    }
Chris@16: private:
Chris@16:    RealType alpha;
Chris@16:    RealType beta;
Chris@16:    RealType ratio; // Difference from variance / variance, so fractional.
Chris@16: };
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: RealType chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom(
Chris@16:    RealType difference_from_variance,
Chris@16:    RealType alpha,
Chris@16:    RealType beta,
Chris@16:    RealType variance,
Chris@16:    RealType hint)
Chris@16: {
Chris@16:    static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";
Chris@16:    // Check for domain errors:
Chris@16:    RealType error_result;
Chris@16:    if(false ==
Chris@16:      detail::check_probability(function, alpha, &error_result, Policy())
Chris@16:      && detail::check_probability(function, beta, &error_result, Policy()))
Chris@16:    { // Either probability is outside 0 to 1.
Chris@16:       return error_result;
Chris@16:    }
Chris@16: 
Chris@16:    if(hint <= 0)
Chris@16:    { // No hint given, so guess df = 1.
Chris@16:       hint = 1;
Chris@16:    }
Chris@16: 
Chris@16:    detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);
Chris@16:    tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
Chris@16:    boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
Chris@16:    std::pair<RealType, RealType> r =
Chris@16:      tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
Chris@16:    RealType result = r.first + (r.second - r.first) / 2;
Chris@16:    if(max_iter >= policies::get_max_root_iterations<Policy>())
Chris@16:    {
Chris@16:       policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
Chris@16:          " either there is no answer to how many degrees of freedom are required"
Chris@16:          " or the answer is infinite.  Current best guess is %1%", result, Policy());
Chris@16:    }
Chris@16:    return result;
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_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP