SV platform dependency builds

//  Copyright John Maddock 2006.

//  Copyright Paul A. Bristow 2006, 2012, 2017.

//  Copyright Thomas Mang 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_STUDENTS_T_HPP

#define BOOST_STATS_STUDENTS_T_HPP

// http://en.wikipedia.org/wiki/Student%27s_t_distribution

// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3664.htm

#include <boost/math/distributions/fwd.hpp>

#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x).

#include <boost/math/distributions/complement.hpp>

#include <boost/math/distributions/detail/common_error_handling.hpp>

#include <boost/math/distributions/normal.hpp> 

#include <utility>

#ifdef BOOST_MSVC

# pragma warning(push)

# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).

#endif

namespace boost { namespace math {

template <class RealType = double, class Policy = policies::policy<> >

class students_t_distribution

{

public:

   typedef RealType value_type;

   typedef Policy policy_type;

   students_t_distribution(RealType df) : df_(df)

   { // Constructor.

      RealType result;

      detail::check_df_gt0_to_inf( // Checks that df > 0 or df == inf.

         "boost::math::students_t_distribution<%1%>::students_t_distribution", df_, &result, Policy());

   } // students_t_distribution

   RealType degrees_of_freedom()const

   {

      return df_;

   }

   // Parameter estimation:

   static RealType find_degrees_of_freedom(

      RealType difference_from_mean,

      RealType alpha,

      RealType beta,

      RealType sd,

      RealType hint = 100);

private:

   // Data member:

   RealType df_;  // degrees of freedom is a real number > 0 or +infinity.

};

typedef students_t_distribution<double> students_t; // Convenience typedef for double version.

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> range(const students_t_distribution<RealType, Policy>& /*dist*/)

{ // Range of permissible values for random variable x.

  // Now including infinity.

   using boost::math::tools::max_value;

   //return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());

   return std::pair<RealType, RealType>(((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>()), ((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? +std::numeric_limits<RealType>::infinity() : +max_value<RealType>()));

}

template <class RealType, class Policy>

inline const std::pair<RealType, RealType> support(const students_t_distribution<RealType, Policy>& /*dist*/)

{ // Range of supported values for random variable x.

  // Now including infinity.

   // 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>());

   return std::pair<RealType, RealType>(((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>()), ((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? +std::numeric_limits<RealType>::infinity() : +max_value<RealType>()));

}

template <class RealType, class Policy>

inline RealType pdf(const students_t_distribution<RealType, Policy>& dist, const RealType& x)

{

   BOOST_FPU_EXCEPTION_GUARD

   BOOST_MATH_STD_USING  // for ADL of std functions.

   RealType error_result;

   if(false == detail::check_x_not_NaN(

      "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy()))

      return error_result;

   RealType df = dist.degrees_of_freedom();

   if(false == detail::check_df_gt0_to_inf( // Check that df > 0 or == +infinity.

      "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy()))

      return error_result;

   RealType result;

   if ((boost::math::isinf)(x))

   { // - or +infinity.

     result = static_cast<RealType>(0);

     return result;

   }

   RealType limit = policies::get_epsilon<RealType, Policy>();

   // Use policies so that if policy requests lower precision, 

   // then get the normal distribution approximation earlier.

   limit = static_cast<RealType>(1) / limit; // 1/eps

   // for 64-bit double 1/eps = 4503599627370496

   if (df > limit)

   { // Special case for really big degrees_of_freedom > 1 / eps 

     // - use normal distribution which is much faster and more accurate.

     normal_distribution<RealType, Policy> n(0, 1); 

     result = pdf(n, x);

   }

   else

   { // 

     RealType basem1 = x * x / df;

     if(basem1 < 0.125)

     {

        result = exp(-boost::math::log1p(basem1, Policy()) * (1+df) / 2);

     }

     else

     {

        result = pow(1 / (1 + basem1), (df + 1) / 2);

     }

     result /= sqrt(df) * boost::math::beta(df / 2, RealType(0.5f), Policy());

   }

   return result;

} // pdf

template <class RealType, class Policy>

inline RealType cdf(const students_t_distribution<RealType, Policy>& dist, const RealType& x)

{

   RealType error_result;

   // degrees_of_freedom > 0 or infinity check:

   RealType df = dist.degrees_of_freedom();

   if (false == detail::check_df_gt0_to_inf(  // Check that df > 0 or == +infinity.

     "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy()))

   {

     return error_result;

   }

   // Check for bad x first.

   if(false == detail::check_x_not_NaN(

      "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy()))

   { 

      return error_result;

   }

   if (x == 0)

   { // Special case with exact result.

     return static_cast<RealType>(0.5);

   }

   if ((boost::math::isinf)(x))

   { // x == - or + infinity, regardless of df.

     return ((x < 0) ? static_cast<RealType>(0) : static_cast<RealType>(1));

   }

   RealType limit = policies::get_epsilon<RealType, Policy>();

   // Use policies so that if policy requests lower precision, 

   // then get the normal distribution approximation earlier.

   limit = static_cast<RealType>(1) / limit; // 1/eps

   // for 64-bit double 1/eps = 4503599627370496

   if (df > limit)

   { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?)

     // - use normal distribution which is much faster and more accurate.

     normal_distribution<RealType, Policy> n(0, 1); 

     RealType result = cdf(n, x);

     return result;

   }

   else

   { // normal df case.

     //

     // Calculate probability of Student's t using the incomplete beta function.

     // probability = ibeta(degrees_of_freedom / 2, 1/2, degrees_of_freedom / (degrees_of_freedom + t*t))

     //

     // However when t is small compared to the degrees of freedom, that formula

     // suffers from rounding error, use the identity formula to work around

     // the problem:

     //

     // I[x](a,b) = 1 - I[1-x](b,a)

     //

     // and:

     //

     //     x = df / (df + t^2)

     //

     // so:

     //

     // 1 - x = t^2 / (df + t^2)

     //

     RealType x2 = x * x;

     RealType probability;

     if(df > 2 * x2)

     {

        RealType z = x2 / (df + x2);

        probability = ibetac(static_cast<RealType>(0.5), df / 2, z, Policy()) / 2;

     }

     else

     {

        RealType z = df / (df + x2);

        probability = ibeta(df / 2, static_cast<RealType>(0.5), z, Policy()) / 2;

     }

     return (x > 0 ? 1   - probability : probability);

  }

} // cdf

template <class RealType, class Policy>

inline RealType quantile(const students_t_distribution<RealType, Policy>& dist, const RealType& p)

{

   BOOST_MATH_STD_USING // for ADL of std functions

   //

   // Obtain parameters:

   RealType probability = p;

   // Check for domain errors:

   RealType df = dist.degrees_of_freedom();

   static const char* function = "boost::math::quantile(const students_t_distribution<%1%>&, %1%)";

   RealType error_result;

   if(false == (detail::check_df_gt0_to_inf( // Check that df > 0 or == +infinity.

      function, df, &error_result, Policy())

         && detail::check_probability(function, probability, &error_result, Policy())))

      return error_result;

   // Special cases, regardless of degrees_of_freedom.

   if (probability == 0)

      return -policies::raise_overflow_error<RealType>(function, 0, Policy());

   if (probability == 1)

     return policies::raise_overflow_error<RealType>(function, 0, Policy());

   if (probability == static_cast<RealType>(0.5))

     return 0;  //

   //

#if 0

   // This next block is disabled in favour of a faster method than

   // incomplete beta inverse, but code retained for future reference:

   //

   // Calculate quantile of Student's t using the incomplete beta function inverse:

   probability = (probability > 0.5) ? 1 - probability : probability;

   RealType t, x, y;

   x = ibeta_inv(degrees_of_freedom / 2, RealType(0.5), 2 * probability, &y);

   if(degrees_of_freedom * y > tools::max_value<RealType>() * x)

      t = tools::overflow_error<RealType>(function);

   else

      t = sqrt(degrees_of_freedom * y / x);

   //

   // Figure out sign based on the size of p:

   //

   if(p < 0.5)

      t = -t;

   return t;

#endif

   //

   // Depending on how many digits RealType has, this may forward

   // to the incomplete beta inverse as above.  Otherwise uses a

   // faster method that is accurate to ~15 digits everywhere

   // and a couple of epsilon at double precision and in the central 

   // region where most use cases will occur...

   //

   return boost::math::detail::fast_students_t_quantile(df, probability, Policy());

} // quantile

template <class RealType, class Policy>

inline RealType cdf(const complemented2_type<students_t_distribution<RealType, Policy>, RealType>& c)

{

   return cdf(c.dist, -c.param);

}

template <class RealType, class Policy>

inline RealType quantile(const complemented2_type<students_t_distribution<RealType, Policy>, RealType>& c)

{

   return -quantile(c.dist, c.param);

}

//

// Parameter estimation follows:

//

namespace detail{

//

// Functors for finding degrees of freedom:

//

template <class RealType, class Policy>

struct sample_size_func

{

   sample_size_func(RealType a, RealType b, RealType s, RealType d)

      : alpha(a), beta(b), ratio(s*s/(d*d)) {}

   RealType operator()(const RealType& df)

   {

      if(df <= tools::min_value<RealType>())

      { // 

         return 1;

      }

      students_t_distribution<RealType, Policy> t(df);

      RealType qa = quantile(complement(t, alpha));

      RealType qb = quantile(complement(t, beta));

      qa += qb;

      qa *= qa;

      qa *= ratio;

      qa -= (df + 1);

      return qa;

   }

   RealType alpha, beta, ratio;

};

}  // namespace detail

template <class RealType, class Policy>

RealType students_t_distribution<RealType, Policy>::find_degrees_of_freedom(

      RealType difference_from_mean,

      RealType alpha,

      RealType beta,

      RealType sd,

      RealType hint)

{

   static const char* function = "boost::math::students_t_distribution<%1%>::find_degrees_of_freedom";

   //

   // Check for domain errors:

   //

   RealType error_result;

   if(false == detail::check_probability(

      function, alpha, &error_result, Policy())

         && detail::check_probability(function, beta, &error_result, Policy()))

      return error_result;

   if(hint <= 0)

      hint = 1;

   detail::sample_size_func<RealType, Policy> f(alpha, beta, sd, difference_from_mean);

   tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());

   boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();

   std::pair<RealType, RealType> r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());

   RealType result = r.first + (r.second - r.first) / 2;

   if(max_iter >= policies::get_max_root_iterations<Policy>())

   {

      return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"

         " either there is no answer to how many degrees of freedom are required"

         " or the answer is infinite.  Current best guess is %1%", result, Policy());

   }

   return result;

}

template <class RealType, class Policy>

inline RealType mode(const students_t_distribution<RealType, Policy>& /*dist*/)

{

  // Assume no checks on degrees of freedom are useful (unlike mean).

   return 0; // Always zero by definition.

}

template <class RealType, class Policy>

inline RealType median(const students_t_distribution<RealType, Policy>& /*dist*/)

{

   // Assume no checks on degrees of freedom are useful (unlike mean).

   return 0; // Always zero by definition.

}

// See section 5.1 on moments at  http://en.wikipedia.org/wiki/Student%27s_t-distribution

template <class RealType, class Policy>

inline RealType mean(const students_t_distribution<RealType, Policy>& dist)

{  // Revised for https://svn.boost.org/trac/boost/ticket/7177

   RealType df = dist.degrees_of_freedom();

   if(((boost::math::isnan)(df)) || (df <= 1) ) 

   { // mean is undefined for moment <= 1!

      return policies::raise_domain_error<RealType>(

      "boost::math::mean(students_t_distribution<%1%> const&, %1%)",

      "Mean is undefined for degrees of freedom < 1 but got %1%.", df, Policy());

      return std::numeric_limits<RealType>::quiet_NaN();

   }

   return 0;

} // mean

template <class RealType, class Policy>

inline RealType variance(const students_t_distribution<RealType, Policy>& dist)

{ // http://en.wikipedia.org/wiki/Student%27s_t-distribution

  // Revised for https://svn.boost.org/trac/boost/ticket/7177

  RealType df = dist.degrees_of_freedom();

  if ((boost::math::isnan)(df) || (df <= 2))

  { // NaN or undefined for <= 2.

     return policies::raise_domain_error<RealType>(

      "boost::math::variance(students_t_distribution<%1%> const&, %1%)",

      "variance is undefined for degrees of freedom <= 2, but got %1%.",

      df, Policy());

    return std::numeric_limits<RealType>::quiet_NaN(); // Undefined.

  }

  if ((boost::math::isinf)(df))

  { // +infinity.

    return 1;

  }

  RealType limit = policies::get_epsilon<RealType, Policy>();

  // Use policies so that if policy requests lower precision, 

  // then get the normal distribution approximation earlier.

  limit = static_cast<RealType>(1) / limit; // 1/eps

  // for 64-bit double 1/eps = 4503599627370496

  if (df > limit)

  { // Special case for really big degrees_of_freedom > 1 / eps.

    return 1;

  }

  else

  {

    return df / (df - 2);

  }

} // variance

template <class RealType, class Policy>

inline RealType skewness(const students_t_distribution<RealType, Policy>& dist)

{

    RealType df = dist.degrees_of_freedom();

   if( ((boost::math::isnan)(df)) || (dist.degrees_of_freedom() <= 3))

   { // Undefined for moment k = 3.

      return policies::raise_domain_error<RealType>(

         "boost::math::skewness(students_t_distribution<%1%> const&, %1%)",

         "Skewness is undefined for degrees of freedom <= 3, but got %1%.",

         dist.degrees_of_freedom(), Policy());

      return std::numeric_limits<RealType>::quiet_NaN();

   }

   return 0; // For all valid df, including infinity.

} // skewness

template <class RealType, class Policy>

inline RealType kurtosis(const students_t_distribution<RealType, Policy>& dist)

{

   RealType df = dist.degrees_of_freedom();

   if(((boost::math::isnan)(df)) || (df <= 4))

   { // Undefined or infinity for moment k = 4.

      return policies::raise_domain_error<RealType>(

       "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)",

       "Kurtosis is undefined for degrees of freedom <= 4, but got %1%.",

        df, Policy());

        return std::numeric_limits<RealType>::quiet_NaN(); // Undefined.

   }

   if ((boost::math::isinf)(df))

   { // +infinity.

     return 3;

   }

   RealType limit = policies::get_epsilon<RealType, Policy>();

   // Use policies so that if policy requests lower precision, 

   // then get the normal distribution approximation earlier.

   limit = static_cast<RealType>(1) / limit; // 1/eps

   // for 64-bit double 1/eps = 4503599627370496

   if (df > limit)

   { // Special case for really big degrees_of_freedom > 1 / eps.

     return 3;

   }

   else

   {

     //return 3 * (df - 2) / (df - 4); re-arranged to

     return 6 / (df - 4) + 3;

   }

} // kurtosis

template <class RealType, class Policy>

inline RealType kurtosis_excess(const students_t_distribution<RealType, Policy>& dist)

{

   // see http://mathworld.wolfram.com/Kurtosis.html

   RealType df = dist.degrees_of_freedom();

   if(((boost::math::isnan)(df)) || (df <= 4))

   { // Undefined or infinity for moment k = 4.

     return policies::raise_domain_error<RealType>(

       "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)",

       "Kurtosis_excess is undefined for degrees of freedom <= 4, but got %1%.",

      df, Policy());

     return std::numeric_limits<RealType>::quiet_NaN(); // Undefined.

   }

   if ((boost::math::isinf)(df))

   { // +infinity.

     return 0;

   }

   RealType limit = policies::get_epsilon<RealType, Policy>();

   // Use policies so that if policy requests lower precision, 

   // then get the normal distribution approximation earlier.

   limit = static_cast<RealType>(1) / limit; // 1/eps

   // for 64-bit double 1/eps = 4503599627370496

   if (df > limit)

   { // Special case for really big degrees_of_freedom > 1 / eps.

     return 0;

   }

   else

   {

     return 6 / (df - 4);

   }

}

} // namespace math

} // namespace boost

#ifdef BOOST_MSVC

# pragma warning(pop)

#endif

// 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_STUDENTS_T_HPP