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/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/skew_normal.hpp (25646B)

//  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 = dist.shape() != 0 ? static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape())) : static_cast<RealType>(0);
    //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 = dist.shape() != 0 ? static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape())) : static_cast<RealType>(0);

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%)";

// 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

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