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

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

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

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

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);
}

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.
}

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.
}

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