beta.hpp

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// boost\math\distributions\beta.hpp

// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2006.

// 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)

// http://en.wikipedia.org/wiki/Beta_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm
// http://mathworld.wolfram.com/BetaDistribution.html

// The Beta Distribution is a continuous probability distribution.
// The beta distribution is used to model events which are constrained to take place
// within an interval defined by maxima and minima,
// so is used extensively in PERT and other project management systems
// to describe the time to completion.
// The cdf of the beta distribution is used as a convenient way
// of obtaining the sum over a set of binomial outcomes.
// The beta distribution is also used in Bayesian statistics.

#ifndef BOOST_MATH_DIST_BETA_HPP
#define BOOST_MATH_DIST_BETA_HPP

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/beta.hpp> // for beta.
#include <boost/math/distributions/complement.hpp> // complements.
#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
#include <boost/math/special_functions/fpclassify.hpp> // isnan.
#include <boost/math/tools/roots.hpp> // for root finding.

#if defined (BOOST_MSVC)
#  pragma warning(push)
#  pragma warning(disable: 4702) // unreachable code
// in domain_error_imp in error_handling
#endif

#include <utility>

namespace boost
{
  namespace math
  {
    namespace beta_detail
    {
      // Common error checking routines for beta distribution functions:
      template <class RealType, class Policy>
      inline bool check_alpha(const char* function, const RealType& alpha, RealType* result, const Policy& pol)
      {
        if(!(boost::math::isfinite)(alpha) || (alpha <= 0))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "Alpha argument is %1%, but must be > 0 !", alpha, pol);
          return false;
        }
        return true;
      } // bool check_alpha

      template <class RealType, class Policy>
      inline bool check_beta(const char* function, const RealType& beta, RealType* result, const Policy& pol)
      {
        if(!(boost::math::isfinite)(beta) || (beta <= 0))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "Beta argument is %1%, but must be > 0 !", beta, pol);
          return false;
        }
        return true;
      } // bool check_beta

      template <class RealType, class Policy>
      inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol)
      {
        if((p < 0) || (p > 1) || !(boost::math::isfinite)(p))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol);
          return false;
        }
        return true;
      } // bool check_prob

      template <class RealType, class Policy>
      inline bool check_x(const char* function, const RealType& x, RealType* result, const Policy& pol)
      {
        if(!(boost::math::isfinite)(x) || (x < 0) || (x > 1))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "x argument is %1%, but must be >= 0 and <= 1 !", x, pol);
          return false;
        }
        return true;
      } // bool check_x

      template <class RealType, class Policy>
      inline bool check_dist(const char* function, const RealType& alpha, const RealType& beta, RealType* result, const Policy& pol)
      { // Check both alpha and beta.
        return check_alpha(function, alpha, result, pol)
          && check_beta(function, beta, result, pol);
      } // bool check_dist

      template <class RealType, class Policy>
      inline bool check_dist_and_x(const char* function, const RealType& alpha, const RealType& beta, RealType x, RealType* result, const Policy& pol)
      {
        return check_dist(function, alpha, beta, result, pol)
          && check_x(function, x, result, pol);
      } // bool check_dist_and_x

      template <class RealType, class Policy>
      inline bool check_dist_and_prob(const char* function, const RealType& alpha, const RealType& beta, RealType p, RealType* result, const Policy& pol)
      {
        return check_dist(function, alpha, beta, result, pol)
          && check_prob(function, p, result, pol);
      } // bool check_dist_and_prob

      template <class RealType, class Policy>
      inline bool check_mean(const char* function, const RealType& mean, RealType* result, const Policy& pol)
      {
        if(!(boost::math::isfinite)(mean) || (mean <= 0))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "mean argument is %1%, but must be > 0 !", mean, pol);
          return false;
        }
        return true;
      } // bool check_mean
      template <class RealType, class Policy>
      inline bool check_variance(const char* function, const RealType& variance, RealType* result, const Policy& pol)
      {
        if(!(boost::math::isfinite)(variance) || (variance <= 0))
        {
          *result = policies::raise_domain_error<RealType>(
            function,
            "variance argument is %1%, but must be > 0 !", variance, pol);
          return false;
        }
        return true;
      } // bool check_variance
    } // namespace beta_detail

    // typedef beta_distribution<double> beta;
    // is deliberately NOT included to avoid a name clash with the beta function.
    // Use beta_distribution<> mybeta(...) to construct type double.

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

      beta_distribution(RealType alpha = 1, RealType beta = 1) : m_alpha(alpha), m_beta(beta)
      {
        RealType result;
        beta_detail::check_dist(
           "boost::math::beta_distribution<%1%>::beta_distribution",
          m_alpha,
          m_beta,
          &result, Policy());
      } // beta_distribution constructor.
      // Accessor functions:
      RealType alpha() const
      {
        return m_alpha;
      }
      RealType beta() const
      { // .
        return m_beta;
      }

      // Estimation of the alpha & beta parameters.
      // http://en.wikipedia.org/wiki/Beta_distribution
      // gives formulae in section on parameter estimation.
      // Also NIST EDA page 3 & 4 give the same.
      // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm
      // http://www.epi.ucdavis.edu/diagnostictests/betabuster.html

      static RealType find_alpha(
        RealType mean, // Expected value of mean.
        RealType variance) // Expected value of variance.
      {
        static const char* function = "boost::math::beta_distribution<%1%>::find_alpha";
        RealType result; // of error checks.
        if(false ==
          beta_detail::check_mean(
          function, mean, &result, Policy())
          &&
          beta_detail::check_variance(
          function, variance, &result, Policy())
          )
        {
          return result;
        }
        return mean * (( (mean * (1 - mean)) / variance)- 1);
      } // RealType find_alpha

      static RealType find_beta(
        RealType mean, // Expected value of mean.
        RealType variance) // Expected value of variance.
      {
        static const char* function = "boost::math::beta_distribution<%1%>::find_beta";
        RealType result; // of error checks.
        if(false ==
          beta_detail::check_mean(
          function, mean, &result, Policy())
          &&
          beta_detail::check_variance(
          function, variance, &result, Policy())
          )
        {
          return result;
        }
        return (1 - mean) * (((mean * (1 - mean)) /variance)-1);
      } //  RealType find_beta

      // Estimate alpha & beta from either alpha or beta, and x and probability.
      // Uses for these parameter estimators are unclear.

      static RealType find_alpha(
        RealType beta, // from beta.
        RealType x, //  x.
        RealType probability) // cdf
      {
        static const char* function = "boost::math::beta_distribution<%1%>::find_alpha";
        RealType result; // of error checks.
        if(false ==
          beta_detail::check_prob(
          function, probability, &result, Policy())
          &&
          beta_detail::check_beta(
          function, beta, &result, Policy())
          &&
          beta_detail::check_x(
          function, x, &result, Policy())
          )
        {
          return result;
        }
        return ibeta_inva(beta, x, probability, Policy());
      } // RealType find_alpha(beta, a, probability)

      static RealType find_beta(
        // ibeta_invb(T b, T x, T p); (alpha, x, cdf,)
        RealType alpha, // alpha.
        RealType x, // probability x.
        RealType probability) // probability cdf.
      {
        static const char* function = "boost::math::beta_distribution<%1%>::find_beta";
        RealType result; // of error checks.
        if(false ==
          beta_detail::check_prob(
          function, probability, &result, Policy())
          &&
          beta_detail::check_alpha(
          function, alpha, &result, Policy())
          &&
          beta_detail::check_x(
          function, x, &result, Policy())
          )
        {
          return result;
        }
        return ibeta_invb(alpha, x, probability, Policy());
      } //  RealType find_beta(alpha, x, probability)

    private: