Chris@102: // boost/math/distributions/arcsine.hpp
Chris@102: 
Chris@102: // Copyright John Maddock 2014.
Chris@102: // Copyright Paul A. Bristow 2014.
Chris@102: 
Chris@102: // Use, modification and distribution are subject to the
Chris@102: // Boost Software License, Version 1.0.
Chris@102: // (See accompanying file LICENSE_1_0.txt
Chris@102: // or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@102: 
Chris@102: // http://en.wikipedia.org/wiki/arcsine_distribution
Chris@102: 
Chris@102: // The arcsine Distribution is a continuous probability distribution.
Chris@102: // http://en.wikipedia.org/wiki/Arcsine_distribution
Chris@102: // http://www.wolframalpha.com/input/?i=ArcSinDistribution
Chris@102: 
Chris@102: // Standard arcsine distribution is a special case of beta distribution with both a & b = one half,
Chris@102: // and 0 <= x <= 1.
Chris@102: 
Chris@102: // It is generalized to include any bounded support a <= x <= b from 0 <= x <= 1
Chris@102: // by Wolfram and Wikipedia,
Chris@102: // but using location and scale parameters by
Chris@102: // Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/index.html
Chris@102: // http://www.math.uah.edu/stat/special/Arcsine.html
Chris@102: // The end-point version is simpler and more obvious, so we implement that.
Chris@102: // TODO Perhaps provide location and scale functions?
Chris@102: 
Chris@102: 
Chris@102: #ifndef BOOST_MATH_DIST_ARCSINE_HPP
Chris@102: #define BOOST_MATH_DIST_ARCSINE_HPP
Chris@102: 
Chris@102: #include <boost/math/distributions/fwd.hpp>
Chris@102: #include <boost/math/distributions/complement.hpp> // complements.
Chris@102: #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks.
Chris@102: #include <boost/math/constants/constants.hpp>
Chris@102: 
Chris@102: #include <boost/math/special_functions/fpclassify.hpp> // isnan.
Chris@102: 
Chris@102: #if defined (BOOST_MSVC)
Chris@102: #  pragma warning(push)
Chris@102: #  pragma warning(disable: 4702) // Unreachable code,
Chris@102: // in domain_error_imp in error_handling.
Chris@102: #endif
Chris@102: 
Chris@102: #include <utility>
Chris@102: #include <exception>  // For std::domain_error.
Chris@102: 
Chris@102: namespace boost
Chris@102: {
Chris@102:   namespace math
Chris@102:   {
Chris@102:     namespace arcsine_detail
Chris@102:     {
Chris@102:       // Common error checking routines for arcsine distribution functions:
Chris@102:       // Duplicating for x_min and x_max provides specific error messages.
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_x_min(const char* function, const RealType& x, RealType* result, const Policy& pol)
Chris@102:       {
Chris@102:         if (!(boost::math::isfinite)(x))
Chris@102:         {
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             "x_min argument is %1%, but must be finite !", x, pol);
Chris@102:           return false;
Chris@102:         }
Chris@102:         return true;
Chris@102:       } // bool check_x_min
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_x_max(const char* function, const RealType& x, RealType* result, const Policy& pol)
Chris@102:       {
Chris@102:         if (!(boost::math::isfinite)(x))
Chris@102:         {
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             "x_max argument is %1%, but must be finite !", x, pol);
Chris@102:           return false;
Chris@102:         }
Chris@102:         return true;
Chris@102:       } // bool check_x_max
Chris@102: 
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_x_minmax(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
Chris@102:       { // Check x_min < x_max
Chris@102:         if (x_min >= x_max)
Chris@102:         {
Chris@102:           std::string msg = "x_max argument is %1%, but must be > x_min = " + lexical_cast<std::string>(x_min) + "!";
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             msg.c_str(), x_max, pol);
Chris@102:            // "x_max argument is %1%, but must be > x_min !", x_max, pol);
Chris@102:             //  "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. 
Chris@102:           // But would require replication of all helpers functions in /policies/error_handling.hpp for two values,
Chris@102:           // as well as two value versions of raise_error, raise_domain_error and do_format ...
Chris@102:           // so use slightly hacky lexical_cast to string instead.
Chris@102:           return false;
Chris@102:         }
Chris@102:         return true;
Chris@102:       } // bool check_x_minmax
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol)
Chris@102:       {
Chris@102:         if ((p < 0) || (p > 1) || !(boost::math::isfinite)(p))
Chris@102:         {
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol);
Chris@102:           return false;
Chris@102:         }
Chris@102:         return true;
Chris@102:       } // bool check_prob
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_x(const char* function, const RealType& x_min, const RealType& x_max, const RealType& x, RealType* result, const Policy& pol)
Chris@102:       { // Check x finite and x_min < x < x_max.
Chris@102:         if (!(boost::math::isfinite)(x))
Chris@102:         {
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             "x argument is %1%, but must be finite !", x, pol);
Chris@102:           return false;
Chris@102:         }
Chris@102:         if ((x < x_min) || (x > x_max))
Chris@102:         {
Chris@102:           // std::cout << x_min << ' ' << x << x_max << std::endl;
Chris@102:           *result = policies::raise_domain_error<RealType>(
Chris@102:             function,
Chris@102:             "x argument is %1%, but must be x_min < x < x_max !", x, pol);
Chris@102:           // For example:
Chris@102:           // Error in function boost::math::pdf(arcsine_distribution<double> const&, double) : x argument is -1.01, but must be x_min < x < x_max !
Chris@102:           // TODO Perhaps show values of x_min and x_max?
Chris@102:           return false;
Chris@102:         }
Chris@102:         return true;
Chris@102:       } // bool check_x
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_dist(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
Chris@102:       { // Check both x_min and x_max finite, and x_min  < x_max.
Chris@102:         return check_x_min(function, x_min, result, pol)
Chris@102:             && check_x_max(function, x_max, result, pol)
Chris@102:             && check_x_minmax(function, x_min, x_max, result, pol);
Chris@102:       } // bool check_dist
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_dist_and_x(const char* function, const RealType& x_min, const RealType& x_max, RealType x, RealType* result, const Policy& pol)
Chris@102:       {
Chris@102:         return check_dist(function, x_min, x_max, result, pol)
Chris@102:           && arcsine_detail::check_x(function, x_min, x_max, x, result, pol);
Chris@102:       } // bool check_dist_and_x
Chris@102: 
Chris@102:       template <class RealType, class Policy>
Chris@102:       inline bool check_dist_and_prob(const char* function, const RealType& x_min, const RealType& x_max, RealType p, RealType* result, const Policy& pol)
Chris@102:       {
Chris@102:         return check_dist(function, x_min, x_max, result, pol)
Chris@102:           && check_prob(function, p, result, pol);
Chris@102:       } // bool check_dist_and_prob
Chris@102: 
Chris@102:     } // namespace arcsine_detail
Chris@102: 
Chris@102:     template <class RealType = double, class Policy = policies::policy<> >
Chris@102:     class arcsine_distribution
Chris@102:     {
Chris@102:     public:
Chris@102:       typedef RealType value_type;
Chris@102:       typedef Policy policy_type;
Chris@102: 
Chris@102:       arcsine_distribution(RealType x_min = 0, RealType x_max = 1) : m_x_min(x_min), m_x_max(x_max)
Chris@102:       { // Default beta (alpha = beta = 0.5) is standard arcsine with x_min = 0, x_max = 1.
Chris@102:         // Generalized to allow x_min and x_max to be specified.
Chris@102:         RealType result;
Chris@102:         arcsine_detail::check_dist(
Chris@102:           "boost::math::arcsine_distribution<%1%>::arcsine_distribution",
Chris@102:           m_x_min,
Chris@102:           m_x_max,
Chris@102:           &result, Policy());
Chris@102:       } // arcsine_distribution constructor.
Chris@102:       // Accessor functions:
Chris@102:       RealType x_min() const
Chris@102:       {
Chris@102:         return m_x_min;
Chris@102:       }
Chris@102:       RealType x_max() const
Chris@102:       {
Chris@102:         return m_x_max;
Chris@102:       }
Chris@102: 
Chris@102:     private:
Chris@102:       RealType m_x_min; // Two x min and x max parameters of the arcsine distribution.
Chris@102:       RealType m_x_max;
Chris@102:     }; // template <class RealType, class Policy> class arcsine_distribution
Chris@102: 
Chris@102:     // Convenient typedef to construct double version.
Chris@102:     typedef arcsine_distribution<double> arcsine;
Chris@102: 
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline const std::pair<RealType, RealType> range(const arcsine_distribution<RealType, Policy>&  dist)
Chris@102:     { // Range of permissible values for random variable x.
Chris@102:       using boost::math::tools::max_value;
Chris@102:       return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max()));
Chris@102:     }
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline const std::pair<RealType, RealType> support(const arcsine_distribution<RealType, Policy>&  dist)
Chris@102:     { // Range of supported values for random variable x.
Chris@102:       // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@102:       return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max()));
Chris@102:     }
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType mean(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     { // Mean of arcsine distribution .
Chris@102:       RealType result;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::mean(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       return  (x_min + x_max) / 2;
Chris@102:     } // mean
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType variance(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     { // Variance of standard arcsine distribution = (1-0)/8 = 0.125.
Chris@102:       RealType result;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::variance(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       return  (x_max - x_min) * (x_max - x_min) / 8;
Chris@102:     } // variance
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType mode(const arcsine_distribution<RealType, Policy>& /* dist */)
Chris@102:     { //There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1,
Chris@102:       // so instead we raise the exception domain_error.
Chris@102:       return policies::raise_domain_error<RealType>(
Chris@102:         "boost::math::mode(arcsine_distribution<%1%>&)",
Chris@102:         "The arcsine distribution has two modes at x_min and x_max: "
Chris@102:         "so the return value is %1%.",
Chris@102:         std::numeric_limits<RealType>::quiet_NaN(), Policy());
Chris@102:     } // mode
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType median(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     { // Median of arcsine distribution (a + b) / 2 == mean.
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102:       RealType result;
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::median(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       return  (x_min + x_max) / 2;
Chris@102:     }
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     {
Chris@102:       RealType result;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::skewness(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       return 0;
Chris@102:     } // skewness
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     {
Chris@102:       RealType result;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       result = -3;
Chris@102:       return  result / 2;
Chris@102:     } // kurtosis_excess
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist)
Chris@102:     {
Chris@102:       RealType result;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       if (false == arcsine_detail::check_dist(
Chris@102:         "boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )",
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         &result, Policy())
Chris@102:         )
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102: 
Chris@102:       return 3 + kurtosis_excess(dist);
Chris@102:     } // kurtosis
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType pdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& xx)
Chris@102:     { // Probability Density/Mass Function arcsine.
Chris@102:       BOOST_FPU_EXCEPTION_GUARD
Chris@102:       BOOST_MATH_STD_USING // For ADL of std functions.
Chris@102: 
Chris@102:       static const char* function = "boost::math::pdf(arcsine_distribution<%1%> const&, %1%)";
Chris@102: 
Chris@102:       RealType lo = dist.x_min();
Chris@102:       RealType hi = dist.x_max();
Chris@102:       RealType x = xx;
Chris@102: 
Chris@102:       // Argument checks:
Chris@102:       RealType result = 0; 
Chris@102:       if (false == arcsine_detail::check_dist_and_x(
Chris@102:         function,
Chris@102:         lo, hi, x,
Chris@102:         &result, Policy()))
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       using boost::math::constants::pi;
Chris@102:       result = static_cast<RealType>(1) / (pi<RealType>() * sqrt((x - lo) * (hi - x)));
Chris@102:       return result;
Chris@102:     } // pdf
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType cdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& x)
Chris@102:     { // Cumulative Distribution Function arcsine.
Chris@102:       BOOST_MATH_STD_USING // For ADL of std functions.
Chris@102: 
Chris@102:       static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
Chris@102: 
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       // Argument checks:
Chris@102:       RealType result = 0;
Chris@102:       if (false == arcsine_detail::check_dist_and_x(
Chris@102:         function,
Chris@102:         x_min, x_max, x,
Chris@102:         &result, Policy()))
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       // Special cases:
Chris@102:       if (x == x_min)
Chris@102:       {
Chris@102:         return 0;
Chris@102:       }
Chris@102:       else if (x == x_max)
Chris@102:       {
Chris@102:         return 1;
Chris@102:       }
Chris@102:       using boost::math::constants::pi;
Chris@102:       result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
Chris@102:       return result;
Chris@102:     } // arcsine cdf
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType cdf(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
Chris@102:     { // Complemented Cumulative Distribution Function arcsine.
Chris@102:       BOOST_MATH_STD_USING // For ADL of std functions.
Chris@102:       static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
Chris@102: 
Chris@102:       RealType x = c.param;
Chris@102:       arcsine_distribution<RealType, Policy> const& dist = c.dist;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102: 
Chris@102:       // Argument checks:
Chris@102:       RealType result = 0;
Chris@102:       if (false == arcsine_detail::check_dist_and_x(
Chris@102:         function,
Chris@102:         x_min, x_max, x,
Chris@102:         &result, Policy()))
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       if (x == x_min)
Chris@102:       {
Chris@102:         return 0;
Chris@102:       }
Chris@102:       else if (x == x_max)
Chris@102:       {
Chris@102:         return 1;
Chris@102:       }
Chris@102:       using boost::math::constants::pi;
Chris@102:       // Naive version x = 1 - x;
Chris@102:       // result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
Chris@102:       // is less accurate, so use acos instead of asin for complement.
Chris@102:       result = static_cast<RealType>(2) * acos(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
Chris@102:       return result;
Chris@102:     } // arcine ccdf
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType quantile(const arcsine_distribution<RealType, Policy>& dist, const RealType& p)
Chris@102:     { 
Chris@102:       // Quantile or Percent Point arcsine function or
Chris@102:       // Inverse Cumulative probability distribution function CDF.
Chris@102:       // Return x (0 <= x <= 1),
Chris@102:       // for a given probability p (0 <= p <= 1).
Chris@102:       // These functions take a probability as an argument
Chris@102:       // and return a value such that the probability that a random variable x
Chris@102:       // will be less than or equal to that value
Chris@102:       // is whatever probability you supplied as an argument.
Chris@102:       BOOST_MATH_STD_USING // For ADL of std functions.
Chris@102: 
Chris@102:       using boost::math::constants::half_pi;
Chris@102: 
Chris@102:       static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
Chris@102: 
Chris@102:       RealType result = 0; // of argument checks:
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102:       if (false == arcsine_detail::check_dist_and_prob(
Chris@102:         function,
Chris@102:         x_min, x_max, p,
Chris@102:         &result, Policy()))
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       // Special cases:
Chris@102:       if (p == 0)
Chris@102:       {
Chris@102:         return 0;
Chris@102:       }
Chris@102:       if (p == 1)
Chris@102:       {
Chris@102:         return 1;
Chris@102:       }
Chris@102: 
Chris@102:       RealType sin2hpip = sin(half_pi<RealType>() * p);
Chris@102:       RealType sin2hpip2 = sin2hpip * sin2hpip;
Chris@102:       result = -x_min * sin2hpip2 + x_min + x_max * sin2hpip2;
Chris@102: 
Chris@102:       return result;
Chris@102:     } // quantile
Chris@102: 
Chris@102:     template <class RealType, class Policy>
Chris@102:     inline RealType quantile(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
Chris@102:     { 
Chris@102:       // Complement Quantile or Percent Point arcsine function.
Chris@102:       // Return the number of expected x for a given
Chris@102:       // complement of the probability q.
Chris@102:       BOOST_MATH_STD_USING // For ADL of std functions.
Chris@102: 
Chris@102:       using boost::math::constants::half_pi;
Chris@102:       static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
Chris@102: 
Chris@102:       // Error checks:
Chris@102:       RealType q = c.param;
Chris@102:       const arcsine_distribution<RealType, Policy>& dist = c.dist;
Chris@102:       RealType result = 0;
Chris@102:       RealType x_min = dist.x_min();
Chris@102:       RealType x_max = dist.x_max();
Chris@102:       if (false == arcsine_detail::check_dist_and_prob(
Chris@102:         function,
Chris@102:         x_min,
Chris@102:         x_max,
Chris@102:         q,
Chris@102:         &result, Policy()))
Chris@102:       {
Chris@102:         return result;
Chris@102:       }
Chris@102:       // Special cases:
Chris@102:       if (q == 1)
Chris@102:       {
Chris@102:         return 0;
Chris@102:       }
Chris@102:       if (q == 0)
Chris@102:       {
Chris@102:         return 1;
Chris@102:       }
Chris@102:       // Naive RealType p = 1 - q; result = sin(half_pi<RealType>() * p); loses accuracy, so use a cos alternative instead.
Chris@102:       //result = cos(half_pi<RealType>() * q); // for arcsine(0,1)
Chris@102:       //result = result * result;
Chris@102:       // For generalized arcsine:
Chris@102:       RealType cos2hpip = cos(half_pi<RealType>() * q);
Chris@102:       RealType cos2hpip2 = cos2hpip * cos2hpip;
Chris@102:       result = -x_min * cos2hpip2 + x_min + x_max * cos2hpip2;
Chris@102: 
Chris@102:       return result;
Chris@102:     } // Quantile Complement
Chris@102: 
Chris@102:   } // namespace math
Chris@102: } // namespace boost
Chris@102: 
Chris@102: // This include must be at the end, *after* the accessors
Chris@102: // for this distribution have been defined, in order to
Chris@102: // keep compilers that support two-phase lookup happy.
Chris@102: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@102: 
Chris@102: #if defined (BOOST_MSVC)
Chris@102: # pragma warning(pop)
Chris@102: #endif
Chris@102: 
Chris@102: #endif // BOOST_MATH_DIST_ARCSINE_HPP