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/* boost random/inverse_gaussian_distribution.hpp header file
*
* Copyright Young Geun Kim 2025
* Distributed under 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)
*
* See http://www.boost.org for most recent version including documentation.
*
* $Id$
*/
#ifndef BOOST_RANDOM_INVERSE_GAUSSIAN_DISTRIBUTION_HPP
#define BOOST_RANDOM_INVERSE_GAUSSIAN_DISTRIBUTION_HPP
#include <boost/config/no_tr1/cmath.hpp>
#include <istream>
#include <iosfwd>
#include <limits>
#include <boost/assert.hpp>
#include <boost/limits.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/operators.hpp>
#include <boost/random/uniform_01.hpp>
#include <boost/random/chi_squared_distribution.hpp>
namespace boost {
namespace random {
/**
* The inverse gaussian distribution is a real-valued distribution with
* two parameters alpha (mean) and beta (shape). It produced values > 0.
*
* It has
* \f$\displaystyle p(x) = \sqrt{\beta / (2 \pi x^3)} \exp(-\frac{\beta (x - \alpha)^2}{2 \alpha^2 x})$.
*
* The algorithm used is from
*
* @blockquote
* "Generating Random Variates Using Transformations with Multiple Roots",
* Michael, J. R., Schucany, W. R. and Haas, R. W.,
* The American Statistician,
* Volume 30, Issue 2, 1976, Pages 88 - 90
* @endblockquote
*/
template<class RealType = double>
class inverse_gaussian_distribution
{
public:
typedef RealType result_type;
typedef RealType input_type;
class param_type {
public:
typedef inverse_gaussian_distribution distribution_type;
/**
* Constructs a @c param_type object from the "alpha" and "beta"
* parameters.
*
* Requires: alpha > 0 && beta > 0
*/
explicit param_type(RealType alpha_arg = RealType(1.0),
RealType beta_arg = RealType(1.0))
: _alpha(alpha_arg), _beta(beta_arg)
{
BOOST_ASSERT(alpha_arg > 0);
BOOST_ASSERT(beta_arg > 0);
}
/** Returns the "alpha" parameter of the distribution. */
RealType alpha() const { return _alpha; }
/** Returns the "beta" parameter of the distribution. */
RealType beta() const { return _beta; }
/** Writes a @c param_type to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
{ os << parm._alpha << ' ' << parm._beta; return os; }
/** Reads a @c param_type from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
{ is >> parm._alpha >> std::ws >> parm._beta; return is; }
/** Returns true if the two sets of parameters are the same. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
{ return lhs._alpha == rhs._alpha && lhs._beta == rhs._beta; }
/** Returns true if the two sets fo parameters are different. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
private:
RealType _alpha;
RealType _beta;
};
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
BOOST_STATIC_ASSERT(!std::numeric_limits<RealType>::is_integer);
#endif
/**
* Constructs an @c inverse_gaussian_distribution from its "alpha" and "beta" parameters.
*
* Requires: alpha > 0, beta > 0
*/
explicit inverse_gaussian_distribution(RealType alpha_arg = RealType(1.0),
RealType beta_arg = RealType(1.0))
: _alpha(alpha_arg), _beta(beta_arg)
{
BOOST_ASSERT(alpha_arg > 0);
BOOST_ASSERT(beta_arg > 0);
init();
}
/** Constructs an @c inverse_gaussian_distribution from its parameters. */
explicit inverse_gaussian_distribution(const param_type& parm)
: _alpha(parm.alpha()), _beta(parm.beta())
{
init();
}
/**
* Returns a random variate distributed according to the
* inverse gaussian distribution.
*/
template<class URNG>
RealType operator()(URNG& urng) const
{
#ifndef BOOST_NO_STDC_NAMESPACE
using std::sqrt;
#endif
RealType w = _alpha * chi_squared_distribution<RealType>(result_type(1))(urng);
RealType cand = _alpha + _c * (w - sqrt(w * (result_type(4) * _beta + w)));
RealType u = uniform_01<RealType>()(urng);
if (u < _alpha / (_alpha + cand)) {
return cand;
}
return _alpha * _alpha / cand;
}
/**
* Returns a random variate distributed accordint to the beta
* distribution with parameters specified by @c param.
*/
template<class URNG>
RealType operator()(URNG& urng, const param_type& parm) const
{
return inverse_gaussian_distribution(parm)(urng);
}
/** Returns the "alpha" parameter of the distribution. */
RealType alpha() const { return _alpha; }
/** Returns the "beta" parameter of the distribution. */
RealType beta() const { return _beta; }
/** Returns the smallest value that the distribution can produce. */
RealType min BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return RealType(0.0); }
/** Returns the largest value that the distribution can produce. */
RealType max BOOST_PREVENT_MACRO_SUBSTITUTION () const
{ return (std::numeric_limits<RealType>::infinity)(); }
/** Returns the parameters of the distribution. */
param_type param() const { return param_type(_alpha, _beta); }
/** Sets the parameters of the distribution. */
void param(const param_type& parm)
{
_alpha = parm.alpha();
_beta = parm.beta();
init();
}
/**
* Effects: Subsequent uses of the distribution do not depend
* on values produced by any engine prior to invoking reset.
*/
void reset() { }
/** Writes an @c inverse_gaussian_distribution to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, inverse_gaussian_distribution, wd)
{
os << wd.param();
return os;
}
/** Reads an @c inverse_gaussian_distribution from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, inverse_gaussian_distribution, wd)
{
param_type parm;
if(is >> parm) {
wd.param(parm);
}
return is;
}
/**
* Returns true if the two instances of @c inverse_gaussian_distribution will
* return identical sequences of values given equal generators.
*/
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(inverse_gaussian_distribution, lhs, rhs)
{ return lhs._alpha == rhs._alpha && lhs._beta == rhs._beta; }
/**
* Returns true if the two instances of @c inverse_gaussian_distribution will
* return different sequences of values given equal generators.
*/
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(inverse_gaussian_distribution)
private:
result_type _alpha;
result_type _beta;
// some data precomputed from the parameters
result_type _c;
void init()
{
_c = _alpha / (result_type(2) * _beta);
}
};
} // namespace random
using random::inverse_gaussian_distribution;
} // namespace boost
#endif // BOOST_RANDOM_INVERSE_GAUSSIAN_DISTRIBUTION_HPP