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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 #include #include #include #include #include #include #include #include #include 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 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::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 RealType operator()(URNG& urng) const { #ifndef BOOST_NO_STDC_NAMESPACE using std::sqrt; #endif RealType w = _alpha * chi_squared_distribution(result_type(1))(urng); RealType cand = _alpha + _c * (w - sqrt(w * (result_type(4) * _beta + w))); RealType u = uniform_01()(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 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::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