FM / distributions

/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/triangular.hpp (18407B)

//  Copyright John Maddock 2006, 2007.
//  Copyright Paul A. Bristow 2006, 2007.
//  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_TRIANGULAR_HPP
#define BOOST_STATS_TRIANGULAR_HPP

// http://mathworld.wolfram.com/TriangularDistribution.html
// Note that the 'constructors' defined by Wolfram are difference from those here,
// for example
// N[variance[triangulardistribution{1, +2}, 1.5], 50] computes 
// 0.041666666666666666666666666666666666666666666666667
// TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2)

// http://en.wikipedia.org/wiki/Triangular_distribution

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/math/distributions/complement.hpp>
#include <boost/math/constants/constants.hpp>

#include <utility>

namespace boost{ namespace math
{
  namespace detail
  {
    template <class RealType, class Policy>
    inline bool check_triangular_lower(
      const char* function,
      RealType lower,
      RealType* result, const Policy& pol)
    {
      if((boost::math::isfinite)(lower))
      { // Any finite value is OK.
        return true;
      }
      else
      { // Not finite: infinity or NaN.
        *result = policies::raise_domain_error<RealType>(
          function,
          "Lower parameter is %1%, but must be finite!", lower, pol);
        return false;
      }
    } // bool check_triangular_lower(

template <class RealType, class Policy>
    inline bool check_triangular_mode(
      const char* function,
      RealType mode,
      RealType* result, const Policy& pol)
    {
      if((boost::math::isfinite)(mode))
      { // any finite value is OK.
        return true;
      }
      else
      { // Not finite: infinity or NaN.
        *result = policies::raise_domain_error<RealType>(
          function,
          "Mode parameter is %1%, but must be finite!", mode, pol);
        return false;
      }
    } // bool check_triangular_mode(

template <class RealType, class Policy>
    inline bool check_triangular_upper(
      const char* function,
      RealType upper,
      RealType* result, const Policy& pol)
    {
      if((boost::math::isfinite)(upper))
      { // any finite value is OK.
        return true;
      }
      else
      { // Not finite: infinity or NaN.
        *result = policies::raise_domain_error<RealType>(
          function,
          "Upper parameter is %1%, but must be finite!", upper, pol);
        return false;
      }
    } // bool check_triangular_upper(

template <class RealType, class Policy>
    inline bool check_triangular_x(
      const char* function,
      RealType const& x,
      RealType* result, const Policy& pol)
    {
      if((boost::math::isfinite)(x))
      { // Any finite value is OK
        return true;
      }
      else
      { // Not finite: infinity or NaN.
        *result = policies::raise_domain_error<RealType>(
          function,
          "x parameter is %1%, but must be finite!", x, pol);
        return false;
      }
    } // bool check_triangular_x

template <class RealType, class Policy>
    inline bool check_triangular(
      const char* function,
      RealType lower,
      RealType mode,
      RealType upper,
      RealType* result, const Policy& pol)
    {
      if ((check_triangular_lower(function, lower, result, pol) == false)
        || (check_triangular_mode(function, mode, result, pol) == false)
        || (check_triangular_upper(function, upper, result, pol) == false))
      { // Some parameter not finite.
        return false;
      }
      else if (lower >= upper) // lower == upper NOT useful.
      { // lower >= upper.
        *result = policies::raise_domain_error<RealType>(
          function,
          "lower parameter is %1%, but must be less than upper!", lower, pol);
        return false;
      }
      else
      { // Check lower <= mode <= upper.
        if (mode < lower)
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "mode parameter is %1%, but must be >= than lower!", lower, pol);
          return false;
        }
        if (mode > upper)
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "mode parameter is %1%, but must be <= than upper!", upper, pol);
          return false;
        }
        return true; // All OK.
      }
    } // bool check_triangular
  } // namespace detail

template <class RealType = double, class Policy = policies::policy<> >
  class triangular_distribution
  {
  public:
    typedef RealType value_type;
    typedef Policy policy_type;

triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1)
      : m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor.
    { // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1,
      // has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2
      // But this -1, 0, 1 is more useful in most applications to approximate normal distribution,
      // where the central value is the most likely and deviations either side equally likely.
      RealType result;
      detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy());
    }
    // Accessor functions.
    RealType lower()const
    {
      return m_lower;
    }
    RealType mode()const
    {
      return m_mode;
    }
    RealType upper()const
    {
      return m_upper;
    }
  private:
    // Data members:
    RealType m_lower;  // distribution lower aka a
    RealType m_mode;  // distribution mode aka c
    RealType m_upper;  // distribution upper aka b
  }; // class triangular_distribution

typedef triangular_distribution<double> triangular;

template <class RealType, class Policy>
  inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */)
  { // Range of permissible values for random variable x.
    using boost::math::tools::max_value;
    return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
  }

template <class RealType, class Policy>
  inline const std::pair<RealType, RealType> support(const triangular_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.
    return std::pair<RealType, RealType>(dist.lower(), dist.upper());
  }

template <class RealType, class Policy>
  RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
  {
    static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_triangular_x(function, x, &result, Policy()))
    {
      return result;
    }
    if((x < lower) || (x > upper))
    {
      return 0;
    }
    if (x == lower)
    { // (mode - lower) == 0 which would lead to divide by zero!
      return (mode == lower) ? 2 / (upper - lower) : RealType(0);
    }
    else if (x == upper)
    {
      return (mode == upper) ? 2 / (upper - lower) : RealType(0);
    }
    else if (x <= mode)
    {
      return 2 * (x - lower) / ((upper - lower) * (mode - lower));
    }
    else
    {  // (x > mode)
      return 2 * (upper - x) / ((upper - lower) * (upper - mode));
    }
  } // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)

template <class RealType, class Policy>
  inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)
  {
    static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_triangular_x(function, x, &result, Policy()))
    {
      return result;
    }
    if((x <= lower))
    {
      return 0;
    }
    if (x >= upper)
    {
      return 1;
    }
    // else lower < x < upper
    if (x <= mode)
    {
      return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
    }
    else
    {
      return 1 - (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
    }
  } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x)

template <class RealType, class Policy>
  RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p)
  {
    BOOST_MATH_STD_USING  // for ADL of std functions (sqrt).
    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0; // of checks
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_probability(function, p, &result, Policy()))
    {
      return result;
    }
    if(p == 0)
    {
      return lower;
    }
    if(p == 1)
    {
      return upper;
    }
    RealType p0 = (mode - lower) / (upper - lower);
    RealType q = 1 - p;
    if (p < p0)
    {
      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
    }
    else if (p == p0)
    {
      result = mode;
    }
    else // p > p0
    {
      result = upper - sqrt((upper - lower) * (upper - mode) * q);
    }
    return result;

} // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q)

template <class RealType, class Policy>
  RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
  {
    static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)";
    RealType lower = c.dist.lower();
    RealType mode = c.dist.mode();
    RealType upper = c.dist.upper();
    RealType x = c.param;
    RealType result = 0; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_triangular_x(function, x, &result, Policy()))
    {
      return result;
    }
    if (x <= lower)
    {
      return 1;
    }
    if (x >= upper)
    {
      return 0;
    }
    if (x <= mode)
    {
      return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower));
    }
    else
    {
      return (upper - x) *  (upper - x) / ((upper - lower) * (upper - mode));
    }
  } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)

template <class RealType, class Policy>
  RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)
  {
    BOOST_MATH_STD_USING  // Aid ADL for sqrt.
    static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)";
    RealType l = c.dist.lower();
    RealType m = c.dist.mode();
    RealType u = c.dist.upper();
    RealType q = c.param; // probability 0 to 1.
    RealType result = 0; // of checks.
    if(false == detail::check_triangular(function, l, m, u, &result, Policy()))
    {
      return result;
    }
    if(false == detail::check_probability(function, q, &result, Policy()))
    {
      return result;
    }
    if(q == 0)
    {
      return u;
    }
    if(q == 1)
    {
      return l;
    }
    RealType lower = c.dist.lower();
    RealType mode = c.dist.mode();
    RealType upper = c.dist.upper();

RealType p = 1 - q;
    RealType p0 = (mode - lower) / (upper - lower);
    if(p < p0)
    {
      RealType s = (upper - lower) * (mode - lower);
      s *= p;
      result = sqrt((upper - lower) * (mode - lower) * p) + lower;
    }
    else if (p == p0)
    {
      result = mode;
    }
    else // p > p0
    {
      result = upper - sqrt((upper - lower) * (upper - mode) * q);
    }
    return result;
  } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c)

template <class RealType, class Policy>
  inline RealType mean(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0;  // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return (lower + upper + mode) / 3;
  } // RealType mean(const triangular_distribution<RealType, Policy>& dist)

template <class RealType, class Policy>
  inline RealType variance(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0; // of checks.
    if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18;
  } // RealType variance(const triangular_distribution<RealType, Policy>& dist)

template <class RealType, class Policy>
  inline RealType mode(const triangular_distribution<RealType, Policy>& dist)
  {
    static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)";
    RealType mode = dist.mode();
    RealType result = 0; // of checks.
    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
    { // This should never happen!
      return result;
    }
    return mode;
  } // RealType mode

template <class RealType, class Policy>
  inline RealType median(const triangular_distribution<RealType, Policy>& dist)
  {
    BOOST_MATH_STD_USING // ADL of std functions.
    static const char* function = "boost::math::median(const triangular_distribution<%1%>&)";
    RealType mode = dist.mode();
    RealType result = 0; // of checks.
    if(false == detail::check_triangular_mode(function, mode, &result, Policy()))
    { // This should never happen!
      return result;
    }
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    if (mode >= (upper + lower) / 2)
    {
      return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>();
    }
    else
    {
      return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>();
    }
  } // RealType mode

template <class RealType, class Policy>
  inline RealType skewness(const triangular_distribution<RealType, Policy>& dist)
  {
    BOOST_MATH_STD_USING  // for ADL of std functions
    using namespace boost::math::constants; // for root_two
    static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)";

RealType lower = dist.lower();
    RealType mode = dist.mode();
    RealType upper = dist.upper();
    RealType result = 0; // of checks.
    if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) /
      (5 * pow((lower * lower + upper * upper + mode * mode 
        - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2)));
    // #11768: Skewness formula for triangular distribution is incorrect -  corrected 29 Oct 2015 for release 1.61.
  } // RealType skewness(const triangular_distribution<RealType, Policy>& dist)

template <class RealType, class Policy>
  inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist)
  { // These checks may be belt and braces as should have been checked on construction?
    static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    RealType mode = dist.mode();
    RealType result = 0;  // of checks.
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return static_cast<RealType>(12)/5; //  12/5 = 2.4;
  } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)

template <class RealType, class Policy>
  inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist)
  { // These checks may be belt and braces as should have been checked on construction?
    static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)";
    RealType lower = dist.lower();
    RealType upper = dist.upper();
    RealType mode = dist.mode();
    RealType result = 0;  // of checks.
    if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy()))
    {
      return result;
    }
    return static_cast<RealType>(-3)/5; // - 3/5 = -0.6
    // Assuming mathworld really means kurtosis excess?  Wikipedia now corrected to match this.
  }

template <class RealType, class Policy>
  inline RealType entropy(const triangular_distribution<RealType, Policy>& dist)
  {
    using std::log;
    return constants::half<RealType>() + log((dist.upper() - dist.lower())/2);
  }

} // 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_TRIANGULAR_HPP

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