comparison any/include/boost/math/distributions/skew_normal.hpp @ 160:cff480c41f97

Add some cross-platform Boost headers

+//  Copyright Benjamin Sobotta 2012
+
+//  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_STATS_SKEW_NORMAL_HPP
+#define BOOST_STATS_SKEW_NORMAL_HPP
+
+// http://en.wikipedia.org/wiki/Skew_normal_distribution
+// http://azzalini.stat.unipd.it/SN/
+// Also:
+// Azzalini, A. (1985). "A class of distributions which includes the normal ones".
+// Scand. J. Statist. 12: 171-178.
+
+#include <boost/math/distributions/fwd.hpp> // TODO add skew_normal distribution to fwd.hpp!
+#include <boost/math/special_functions/owens_t.hpp> // Owen's T function
+#include <boost/math/distributions/complement.hpp>
+#include <boost/math/distributions/normal.hpp>
+#include <boost/math/distributions/detail/common_error_handling.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/tools/tuple.hpp>
+#include <boost/math/tools/roots.hpp> // Newton-Raphson
+#include <boost/assert.hpp>
+#include <boost/math/distributions/detail/generic_mode.hpp> // pdf max finder.
+
+#include <utility>
+#include <algorithm> // std::lower_bound, std::distance
+
+namespace boost{ namespace math{
+
+  namespace detail
+  {
+    template <class RealType, class Policy>
+    inline bool check_skew_normal_shape(
+      const char* function,
+      RealType shape,
+      RealType* result,
+      const Policy& pol)
+    {
+      if(!(boost::math::isfinite)(shape))
+      {
+        *result =
+          policies::raise_domain_error<RealType>(function,
+          "Shape parameter is %1%, but must be finite!",
+          shape, pol);
+        return false;
+      }
+      return true;
+    }
+
+  } // namespace detail
+
+  template <class RealType = double, class Policy = policies::policy<> >
+  class skew_normal_distribution
+  {
+  public:
+    typedef RealType value_type;
+    typedef Policy policy_type;
+
+    skew_normal_distribution(RealType l_location = 0, RealType l_scale = 1, RealType l_shape = 0)
+      : location_(l_location), scale_(l_scale), shape_(l_shape)
+    { // Default is a 'standard' normal distribution N01. (shape=0 results in the normal distribution with no skew)
+      static const char* function = "boost::math::skew_normal_distribution<%1%>::skew_normal_distribution";
+
+      RealType result;
+      detail::check_scale(function, l_scale, &result, Policy());
+      detail::check_location(function, l_location, &result, Policy());
+      detail::check_skew_normal_shape(function, l_shape, &result, Policy());
+    }
+
+    RealType location()const
+    { 
+      return location_;
+    }
+
+    RealType scale()const
+    { 
+      return scale_;
+    }
+
+    RealType shape()const
+    { 
+      return shape_;
+    }
+
+
+  private:
+    //
+    // Data members:
+    //
+    RealType location_;  // distribution location.
+    RealType scale_;    // distribution scale.
+    RealType shape_;    // distribution shape.
+  }; // class skew_normal_distribution
+
+  typedef skew_normal_distribution<double> skew_normal;
+
+  template <class RealType, class Policy>
+  inline const std::pair<RealType, RealType> range(const skew_normal_distribution<RealType, Policy>& /*dist*/)
+  { // Range of permissible values for random variable x.
+    using boost::math::tools::max_value;
+    return std::pair<RealType, RealType>(
+       std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), 
+       std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); // - to + max value.
+  }
+
+  template <class RealType, class Policy>
+  inline const std::pair<RealType, RealType> support(const skew_normal_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.
+
+    using boost::math::tools::max_value;
+    return std::pair<RealType, RealType>(-max_value<RealType>(),  max_value<RealType>()); // - to + max value.
+  }
+
+  template <class RealType, class Policy>
+  inline RealType pdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x)
+  {
+    const RealType scale = dist.scale();
+    const RealType location = dist.location();
+    const RealType shape = dist.shape();
+
+    static const char* function = "boost::math::pdf(const skew_normal_distribution<%1%>&, %1%)";
+
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_location(function, location, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+    {
+      return result;
+    }
+    if((boost::math::isinf)(x))
+    {
+       return 0; // pdf + and - infinity is zero.
+    }
+    // Below produces MSVC 4127 warnings, so the above used instead.
+    //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity())
+    //{ // pdf + and - infinity is zero.
+    //  return 0;
+    //}
+    if(false == detail::check_x(function, x, &result, Policy()))
+    {
+      return result;
+    }
+
+    const RealType transformed_x = (x-location)/scale;
+
+    normal_distribution<RealType, Policy> std_normal;
+
+    result = pdf(std_normal, transformed_x) * cdf(std_normal, shape*transformed_x) * 2 / scale;
+
+    return result;
+  } // pdf
+
+  template <class RealType, class Policy>
+  inline RealType cdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x)
+  {
+    const RealType scale = dist.scale();
+    const RealType location = dist.location();
+    const RealType shape = dist.shape();
+
+    static const char* function = "boost::math::cdf(const skew_normal_distribution<%1%>&, %1%)";
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_location(function, location, &result, Policy()))
+    {
+      return result;
+    }
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+    {
+      return result;
+    }
+    if((boost::math::isinf)(x))
+    {
+      if(x < 0) return 0; // -infinity
+      return 1; // + infinity
+    }
+    // These produce MSVC 4127 warnings, so the above used instead.
+    //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
+    //{ // cdf +infinity is unity.
+    //  return 1;
+    //}
+    //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
+    //{ // cdf -infinity is zero.
+    //  return 0;
+    //}
+    if(false == detail::check_x(function, x, &result, Policy()))
+    {
+      return result;
+    }
+
+    const RealType transformed_x = (x-location)/scale;
+
+    normal_distribution<RealType, Policy> std_normal;
+
+    result = cdf(std_normal, transformed_x) - owens_t(transformed_x, shape)*static_cast<RealType>(2);
+
+    return result;
+  } // cdf
+
+  template <class RealType, class Policy>
+  inline RealType cdf(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c)
+  {
+    const RealType scale = c.dist.scale();
+    const RealType location = c.dist.location();
+    const RealType shape = c.dist.shape();
+    const RealType x = c.param;
+
+    static const char* function = "boost::math::cdf(const complement(skew_normal_distribution<%1%>&), %1%)";
+
+    if((boost::math::isinf)(x))
+    {
+      if(x < 0) return 1; // cdf complement -infinity is unity.
+      return 0; // cdf complement +infinity is zero
+    }
+    // These produce MSVC 4127 warnings, so the above used instead.
+    //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity())
+    //{ // cdf complement +infinity is zero.
+    //  return 0;
+    //}
+    //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity())
+    //{ // cdf complement -infinity is unity.
+    //  return 1;
+    //}
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+      return result;
+    if(false == detail::check_location(function, location, &result, Policy()))
+      return result;
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+      return result;
+    if(false == detail::check_x(function, x, &result, Policy()))
+      return result;
+
+    const RealType transformed_x = (x-location)/scale;
+
+    normal_distribution<RealType, Policy> std_normal;
+
+    result = cdf(complement(std_normal, transformed_x)) + owens_t(transformed_x, shape)*static_cast<RealType>(2);
+    return result;
+  } // cdf complement
+
+  template <class RealType, class Policy>
+  inline RealType location(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    return dist.location();
+  }
+
+  template <class RealType, class Policy>
+  inline RealType scale(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    return dist.scale();
+  }
+
+  template <class RealType, class Policy>
+  inline RealType shape(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    return dist.shape();
+  }
+
+  template <class RealType, class Policy>
+  inline RealType mean(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    BOOST_MATH_STD_USING  // for ADL of std functions
+
+    using namespace boost::math::constants;
+
+    //const RealType delta = dist.shape() / sqrt(static_cast<RealType>(1)+dist.shape()*dist.shape());
+
+    //return dist.location() + dist.scale() * delta * root_two_div_pi<RealType>();
+
+    return dist.location() + dist.scale() * dist.shape() / sqrt(pi<RealType>()+pi<RealType>()*dist.shape()*dist.shape()) * root_two<RealType>();
+  }
+
+  template <class RealType, class Policy>
+  inline RealType variance(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    using namespace boost::math::constants;
+
+    const RealType delta2 = static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape()));
+    //const RealType inv_delta2 = static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape());
+
+    RealType variance = dist.scale()*dist.scale()*(static_cast<RealType>(1)-two_div_pi<RealType>()*delta2);
+    //RealType variance = dist.scale()*dist.scale()*(static_cast<RealType>(1)-two_div_pi<RealType>()/inv_delta2);
+
+    return variance;
+  }
+
+  namespace detail
+  {
+    /*
+      TODO No closed expression for mode, so use max of pdf.
+    */
+    
+    template <class RealType, class Policy>
+    inline RealType mode_fallback(const skew_normal_distribution<RealType, Policy>& dist)
+    { // mode.
+        static const char* function = "mode(skew_normal_distribution<%1%> const&)";
+        const RealType scale = dist.scale();
+        const RealType location = dist.location();
+        const RealType shape = dist.shape();
+        
+        RealType result;
+        if(!detail::check_scale(
+          function,
+          scale, &result, Policy())
+          ||
+        !detail::check_skew_normal_shape(
+          function,
+          shape,
+          &result,
+          Policy()))
+        return result;
+
+        if( shape == 0 )
+        {
+          return location;
+        }
+
+        if( shape < 0 )
+        {
+          skew_normal_distribution<RealType, Policy> D(0, 1, -shape);
+          result = mode_fallback(D);
+          result = location-scale*result;
+          return result;
+        }
+        
+        BOOST_MATH_STD_USING
+
+        // 21 elements
+        static const RealType shapes[] = {
+          0.0,
+          1.000000000000000e-004,
+          2.069138081114790e-004,
+          4.281332398719396e-004,
+          8.858667904100824e-004,
+          1.832980710832436e-003,
+          3.792690190732250e-003,
+          7.847599703514606e-003,
+          1.623776739188722e-002,
+          3.359818286283781e-002,
+          6.951927961775606e-002,
+          1.438449888287663e-001,
+          2.976351441631319e-001,
+          6.158482110660261e-001,
+          1.274274985703135e+000,
+          2.636650898730361e+000,
+          5.455594781168514e+000,
+          1.128837891684688e+001,
+          2.335721469090121e+001,
+          4.832930238571753e+001,
+          1.000000000000000e+002};
+
+        // 21 elements
+        static const RealType guess[] = {
+          0.0,
+          5.000050000525391e-005,
+          1.500015000148736e-004,
+          3.500035000350010e-004,
+          7.500075000752560e-004,
+          1.450014500145258e-003,
+          3.050030500305390e-003,
+          6.250062500624765e-003,
+          1.295012950129504e-002,
+          2.675026750267495e-002,
+          5.525055250552491e-002,
+          1.132511325113255e-001,
+          2.249522495224952e-001,
+          3.992539925399257e-001,
+          5.353553535535358e-001,
+          4.954549545495457e-001,
+          3.524535245352451e-001,
+          2.182521825218249e-001,
+          1.256512565125654e-001,
+          6.945069450694508e-002,
+          3.735037350373460e-002
+        };
+
+        const RealType* result_ptr = std::lower_bound(shapes, shapes+21, shape);
+
+        typedef typename std::iterator_traits<RealType*>::difference_type diff_type;
+        
+        const diff_type d = std::distance(shapes, result_ptr);
+        
+        BOOST_ASSERT(d > static_cast<diff_type>(0));
+
+        // refine
+        if(d < static_cast<diff_type>(21)) // shape smaller 100
+        {
+          result = guess[d-static_cast<diff_type>(1)]
+            + (guess[d]-guess[d-static_cast<diff_type>(1)])/(shapes[d]-shapes[d-static_cast<diff_type>(1)])
+            * (shape-shapes[d-static_cast<diff_type>(1)]);
+        }
+        else // shape greater 100
+        {
+          result = 1e-4;
+        }
+
+        skew_normal_distribution<RealType, Policy> helper(0, 1, shape);
+        
+        result = detail::generic_find_mode_01(helper, result, function);
+        
+        result = result*scale + location;
+        
+        return result;
+    } // mode_fallback
+    
+    
+    /*
+     * TODO No closed expression for mode, so use f'(x) = 0
+     */
+    template <class RealType, class Policy>
+    struct skew_normal_mode_functor
+    { 
+      skew_normal_mode_functor(const boost::math::skew_normal_distribution<RealType, Policy> dist)
+        : distribution(dist)
+      {
+      }
+
+      boost::math::tuple<RealType, RealType> operator()(RealType const& x)
+      {
+        normal_distribution<RealType, Policy> std_normal;
+        const RealType shape = distribution.shape();
+        const RealType pdf_x = pdf(distribution, x);
+        const RealType normpdf_x = pdf(std_normal, x);
+        const RealType normpdf_ax = pdf(std_normal, x*shape);
+        RealType fx = static_cast<RealType>(2)*shape*normpdf_ax*normpdf_x - x*pdf_x;
+        RealType dx = static_cast<RealType>(2)*shape*x*normpdf_x*normpdf_ax*(static_cast<RealType>(1) + shape*shape) + pdf_x + x*fx;
+        // return both function evaluation difference f(x) and 1st derivative f'(x).
+        return boost::math::make_tuple(fx, -dx);
+      }
+    private:
+      const boost::math::skew_normal_distribution<RealType, Policy> distribution;
+    };
+    
+  } // namespace detail
+  
+  template <class RealType, class Policy>
+  inline RealType mode(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    const RealType scale = dist.scale();
+    const RealType location = dist.location();
+    const RealType shape = dist.shape();
+
+    static const char* function = "boost::math::mode(const skew_normal_distribution<%1%>&, %1%)";
+
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+      return result;
+    if(false == detail::check_location(function, location, &result, Policy()))
+      return result;
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+      return result;
+
+    if( shape == 0 )
+    {
+      return location;
+    }
+
+    if( shape < 0 )
+    {
+      skew_normal_distribution<RealType, Policy> D(0, 1, -shape);
+      result = mode(D);
+      result = location-scale*result;
+      return result;
+    }
+
+    // 21 elements
+    static const RealType shapes[] = {
+      0.0,
+      static_cast<RealType>(1.000000000000000e-004),
+      static_cast<RealType>(2.069138081114790e-004),
+      static_cast<RealType>(4.281332398719396e-004),
+      static_cast<RealType>(8.858667904100824e-004),
+      static_cast<RealType>(1.832980710832436e-003),
+      static_cast<RealType>(3.792690190732250e-003),
+      static_cast<RealType>(7.847599703514606e-003),
+      static_cast<RealType>(1.623776739188722e-002),
+      static_cast<RealType>(3.359818286283781e-002),
+      static_cast<RealType>(6.951927961775606e-002),
+      static_cast<RealType>(1.438449888287663e-001),
+      static_cast<RealType>(2.976351441631319e-001),
+      static_cast<RealType>(6.158482110660261e-001),
+      static_cast<RealType>(1.274274985703135e+000),
+      static_cast<RealType>(2.636650898730361e+000),
+      static_cast<RealType>(5.455594781168514e+000),
+      static_cast<RealType>(1.128837891684688e+001),
+      static_cast<RealType>(2.335721469090121e+001),
+      static_cast<RealType>(4.832930238571753e+001),
+      static_cast<RealType>(1.000000000000000e+002)
+    };
+
+    // 21 elements
+    static const RealType guess[] = {
+      0.0,
+      static_cast<RealType>(5.000050000525391e-005),
+      static_cast<RealType>(1.500015000148736e-004),
+      static_cast<RealType>(3.500035000350010e-004),
+      static_cast<RealType>(7.500075000752560e-004),
+      static_cast<RealType>(1.450014500145258e-003),
+      static_cast<RealType>(3.050030500305390e-003),
+      static_cast<RealType>(6.250062500624765e-003),
+      static_cast<RealType>(1.295012950129504e-002),
+      static_cast<RealType>(2.675026750267495e-002),
+      static_cast<RealType>(5.525055250552491e-002),
+      static_cast<RealType>(1.132511325113255e-001),
+      static_cast<RealType>(2.249522495224952e-001),
+      static_cast<RealType>(3.992539925399257e-001),
+      static_cast<RealType>(5.353553535535358e-001),
+      static_cast<RealType>(4.954549545495457e-001),
+      static_cast<RealType>(3.524535245352451e-001),
+      static_cast<RealType>(2.182521825218249e-001),
+      static_cast<RealType>(1.256512565125654e-001),
+      static_cast<RealType>(6.945069450694508e-002),
+      static_cast<RealType>(3.735037350373460e-002)
+    };
+
+    const RealType* result_ptr = std::lower_bound(shapes, shapes+21, shape);
+
+    typedef typename std::iterator_traits<RealType*>::difference_type diff_type;
+    
+    const diff_type d = std::distance(shapes, result_ptr);
+    
+    BOOST_ASSERT(d > static_cast<diff_type>(0));
+
+    // TODO: make the search bounds smarter, depending on the shape parameter
+    RealType search_min = 0; // below zero was caught above
+    RealType search_max = 0.55f; // will never go above 0.55
+
+    // refine
+    if(d < static_cast<diff_type>(21)) // shape smaller 100
+    {
+      // it is safe to assume that d > 0, because shape==0.0 is caught earlier
+      result = guess[d-static_cast<diff_type>(1)]
+        + (guess[d]-guess[d-static_cast<diff_type>(1)])/(shapes[d]-shapes[d-static_cast<diff_type>(1)])
+        * (shape-shapes[d-static_cast<diff_type>(1)]);
+    }
+    else // shape greater 100
+    {
+      result = 1e-4f;
+      search_max = guess[19]; // set 19 instead of 20 to have a safety margin because the table may not be exact @ shape=100
+    }
+    
+    const int get_digits = policies::digits<RealType, Policy>();// get digits from policy, 
+    boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations.
+
+    skew_normal_distribution<RealType, Policy> helper(0, 1, shape);
+
+    result = tools::newton_raphson_iterate(detail::skew_normal_mode_functor<RealType, Policy>(helper), result,
+      search_min, search_max, get_digits, m);
+    
+    result = result*scale + location;
+
+    return result;
+  }
+  
+
+  
+  template <class RealType, class Policy>
+  inline RealType skewness(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    BOOST_MATH_STD_USING  // for ADL of std functions
+    using namespace boost::math::constants;
+
+    static const RealType factor = four_minus_pi<RealType>()/static_cast<RealType>(2);
+    const RealType delta = dist.shape() / sqrt(static_cast<RealType>(1)+dist.shape()*dist.shape());
+
+    return factor * pow(root_two_div_pi<RealType>() * delta, 3) /
+      pow(static_cast<RealType>(1)-two_div_pi<RealType>()*delta*delta, static_cast<RealType>(1.5));
+  }
+
+  template <class RealType, class Policy>
+  inline RealType kurtosis(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    return kurtosis_excess(dist)+static_cast<RealType>(3);
+  }
+
+  template <class RealType, class Policy>
+  inline RealType kurtosis_excess(const skew_normal_distribution<RealType, Policy>& dist)
+  {
+    using namespace boost::math::constants;
+
+    static const RealType factor = pi_minus_three<RealType>()*static_cast<RealType>(2);
+
+    const RealType delta2 = static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape()));
+
+    const RealType x = static_cast<RealType>(1)-two_div_pi<RealType>()*delta2;
+    const RealType y = two_div_pi<RealType>() * delta2;
+
+    return factor * y*y / (x*x);
+  }
+
+  namespace detail
+  {
+
+    template <class RealType, class Policy>
+    struct skew_normal_quantile_functor
+    { 
+      skew_normal_quantile_functor(const boost::math::skew_normal_distribution<RealType, Policy> dist, RealType const& p)
+        : distribution(dist), prob(p)
+      {
+      }
+
+      boost::math::tuple<RealType, RealType> operator()(RealType const& x)
+      {
+        RealType c = cdf(distribution, x);
+        RealType fx = c - prob;  // Difference cdf - value - to minimize.
+        RealType dx = pdf(distribution, x); // pdf is 1st derivative.
+        // return both function evaluation difference f(x) and 1st derivative f'(x).
+        return boost::math::make_tuple(fx, dx);
+      }
+    private:
+      const boost::math::skew_normal_distribution<RealType, Policy> distribution;
+      RealType prob; 
+    };
+
+  } // namespace detail
+
+  template <class RealType, class Policy>
+  inline RealType quantile(const skew_normal_distribution<RealType, Policy>& dist, const RealType& p)
+  {
+    const RealType scale = dist.scale();
+    const RealType location = dist.location();
+    const RealType shape = dist.shape();
+
+    static const char* function = "boost::math::quantile(const skew_normal_distribution<%1%>&, %1%)";
+
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+      return result;
+    if(false == detail::check_location(function, location, &result, Policy()))
+      return result;
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+      return result;
+    if(false == detail::check_probability(function, p, &result, Policy()))
+      return result;
+
+    // Compute initial guess via Cornish-Fisher expansion.
+    RealType x = -boost::math::erfc_inv(2 * p, Policy()) * constants::root_two<RealType>();
+
+    // Avoid unnecessary computations if there is no skew.
+    if(shape != 0)
+    {
+      const RealType skew = skewness(dist);
+      const RealType exk = kurtosis_excess(dist);
+
+      x = x + (x*x-static_cast<RealType>(1))*skew/static_cast<RealType>(6)
+      + x*(x*x-static_cast<RealType>(3))*exk/static_cast<RealType>(24)
+      - x*(static_cast<RealType>(2)*x*x-static_cast<RealType>(5))*skew*skew/static_cast<RealType>(36);
+    } // if(shape != 0)
+
+    result = standard_deviation(dist)*x+mean(dist);
+
+    // handle special case of non-skew normal distribution.
+    if(shape == 0)
+      return result;
+
+    // refine the result by numerically searching the root of (p-cdf)
+
+    const RealType search_min = range(dist).first;
+    const RealType search_max = range(dist).second;
+
+    const int get_digits = policies::digits<RealType, Policy>();// get digits from policy, 
+    boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations.
+
+    result = tools::newton_raphson_iterate(detail::skew_normal_quantile_functor<RealType, Policy>(dist, p), result,
+      search_min, search_max, get_digits, m);
+
+    return result;
+  } // quantile
+
+  template <class RealType, class Policy>
+  inline RealType quantile(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c)
+  {
+    const RealType scale = c.dist.scale();
+    const RealType location = c.dist.location();
+    const RealType shape = c.dist.shape();
+
+    static const char* function = "boost::math::quantile(const complement(skew_normal_distribution<%1%>&), %1%)";
+    RealType result = 0;
+    if(false == detail::check_scale(function, scale, &result, Policy()))
+      return result;
+    if(false == detail::check_location(function, location, &result, Policy()))
+      return result;
+    if(false == detail::check_skew_normal_shape(function, shape, &result, Policy()))
+      return result;
+    RealType q = c.param;
+    if(false == detail::check_probability(function, q, &result, Policy()))
+      return result;
+
+    skew_normal_distribution<RealType, Policy> D(-location, scale, -shape);
+
+    result = -quantile(D, q);
+
+    return result;
+  } // quantile
+
+
+} // 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_STATS_SKEW_NORMAL_HPP
+
+