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

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 = "lslboost::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) || !(lslboost::math::isfinite)(chi_square))
   {
      return policies::raise_domain_error<RealType>(
         function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
   }

   return lslboost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy());
} // cdf

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 = "lslboost::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) || !(lslboost::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

inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist)
{
   RealType df = dist.degrees_of_freedom();
   static const char* function = "lslboost::math::mode(const chi_squared_distribution<%1%>&)";
   // Most sources only define mode for df >= 2,
   // but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0;
   // So one could extend the definition of mode thus:
   //if(df < 0)
   //{
   //   return policies::raise_domain_error<RealType>(
   //      function,
   //      "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
   //      df, Policy());
   //}
   //return (df <= 2) ? 0 : df - 2;

   if(df < 2)
      return policies::raise_domain_error<RealType>(
         function,
         "Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
         df, Policy());
   return df - 2;
}

inline RealType kurtosis_excess(const chi_squared_distribution<RealType, Policy>& dist)
{
   RealType df = dist.degrees_of_freedom();
   return 12 / df;
}

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);
}

inline RealType variance(const chi_squared_distribution<RealType, Policy>& dist)
{ // Variance of Chi-Squared distribution = 2v.
  return 2 * dist.degrees_of_freedom();
} // variance

inline RealType mean(const chi_squared_distribution<RealType, Policy>& dist)
{ // Mean of Chi-Squared distribution = v.
  return dist.degrees_of_freedom();
} // mean