/* Copyright 2005 Robert Kern (robert.kern@gmail.com) * * Permission is hereby granted, free of charge, to any person obtaining a * copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be included * in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #ifndef _RK_DISTR_ #define _RK_DISTR_ #include "randomkit.h" #ifdef __cplusplus extern "C" { #endif /* References: * * Devroye, Luc. _Non-Uniform Random Variate Generation_. * Springer-Verlag, New York, 1986. * http://cgm.cs.mcgill.ca/~luc/rnbookindex.html * * Kachitvichyanukul, V. and Schmeiser, B. W. Binomial Random Variate * Generation. Communications of the ACM, 31, 2 (February, 1988) 216. * * Hoermann, W. The Transformed Rejection Method for Generating Poisson Random * Variables. Insurance: Mathematics and Economics, (to appear) * http://citeseer.csail.mit.edu/151115.html * * Marsaglia, G. and Tsang, W. W. A Simple Method for Generating Gamma * Variables. ACM Transactions on Mathematical Software, Vol. 26, No. 3, * September 2000, Pages 363–372. */ /* Normal distribution with mean=loc and standard deviation=scale. */ extern double rk_normal(rk_state *state, double loc, double scale); /* Standard exponential distribution (mean=1) computed by inversion of the * CDF. */ extern double rk_standard_exponential(rk_state *state); /* Exponential distribution with mean=scale. */ extern double rk_exponential(rk_state *state, double scale); /* Uniform distribution on interval [loc, loc+scale). */ extern double rk_uniform(rk_state *state, double loc, double scale); /* Standard gamma distribution with shape parameter. * When shape < 1, the algorithm given by (Devroye p. 304) is used. * When shape == 1, a Exponential variate is generated. * When shape > 1, the small and fast method of (Marsaglia and Tsang 2000) * is used. */ extern double rk_standard_gamma(rk_state *state, double shape); /* Gamma distribution with shape and scale. */ extern double rk_gamma(rk_state *state, double shape, double scale); /* Beta distribution computed by combining two gamma variates (Devroye p. 432). */ extern double rk_beta(rk_state *state, double a, double b); /* Chi^2 distribution computed by transforming a gamma variate (it being a * special case Gamma(df/2, 2)). */ extern double rk_chisquare(rk_state *state, double df); /* Noncentral Chi^2 distribution computed by modifying a Chi^2 variate. */ extern double rk_noncentral_chisquare(rk_state *state, double df, double nonc); /* F distribution computed by taking the ratio of two Chi^2 variates. */ extern double rk_f(rk_state *state, double dfnum, double dfden); /* Noncentral F distribution computed by taking the ratio of a noncentral Chi^2 * and a Chi^2 variate. */ extern double rk_noncentral_f(rk_state *state, double dfnum, double dfden, double nonc); /* Binomial distribution with n Bernoulli trials with success probability p. * When n*p <= 30, the "Second waiting time method" given by (Devroye p. 525) is * used. Otherwise, the BTPE algorithm of (Kachitvichyanukul and Schmeiser 1988) * is used. */ extern long rk_binomial(rk_state *state, long n, double p); /* Binomial distribution using BTPE. */ extern long rk_binomial_btpe(rk_state *state, long n, double p); /* Binomial distribution using inversion and chop-down */ extern long rk_binomial_inversion(rk_state *state, long n, double p); /* Negative binomial distribution computed by generating a Gamma(n, (1-p)/p) * variate Y and returning a Poisson(Y) variate (Devroye p. 543). */ extern long rk_negative_binomial(rk_state *state, double n, double p); /* Poisson distribution with mean=lam. * When lam < 10, a basic algorithm using repeated multiplications of uniform * variates is used (Devroye p. 504). * When lam >= 10, algorithm PTRS from (Hoermann 1992) is used. */ extern long rk_poisson(rk_state *state, double lam); /* Poisson distribution computed by repeated multiplication of uniform variates. */ extern long rk_poisson_mult(rk_state *state, double lam); /* Poisson distribution computer by the PTRS algorithm. */ extern long rk_poisson_ptrs(rk_state *state, double lam); /* Standard Cauchy distribution computed by dividing standard gaussians * (Devroye p. 451). */ extern double rk_standard_cauchy(rk_state *state); /* Standard t-distribution with df degrees of freedom (Devroye p. 445 as * corrected in the Errata). */ extern double rk_standard_t(rk_state *state, double df); /* von Mises circular distribution with center mu and shape kappa on [-pi,pi] * (Devroye p. 476 as corrected in the Errata). */ extern double rk_vonmises(rk_state *state, double mu, double kappa); /* Pareto distribution via inversion (Devroye p. 262) */ extern double rk_pareto(rk_state *state, double a); /* Weibull distribution via inversion (Devroye p. 262) */ extern double rk_weibull(rk_state *state, double a); /* Power distribution via inversion (Devroye p. 262) */ extern double rk_power(rk_state *state, double a); /* Laplace distribution */ extern double rk_laplace(rk_state *state, double loc, double scale); /* Gumbel distribution */ extern double rk_gumbel(rk_state *state, double loc, double scale); /* Logistic distribution */ extern double rk_logistic(rk_state *state, double loc, double scale); /* Log-normal distribution */ extern double rk_lognormal(rk_state *state, double mean, double sigma); /* Rayleigh distribution */ extern double rk_rayleigh(rk_state *state, double mode); /* Wald distribution */ extern double rk_wald(rk_state *state, double mean, double scale); /* Zipf distribution */ extern long rk_zipf(rk_state *state, double a); /* Geometric distribution */ extern long rk_geometric(rk_state *state, double p); extern long rk_geometric_search(rk_state *state, double p); extern long rk_geometric_inversion(rk_state *state, double p); /* Hypergeometric distribution */ extern long rk_hypergeometric(rk_state *state, long good, long bad, long sample); extern long rk_hypergeometric_hyp(rk_state *state, long good, long bad, long sample); extern long rk_hypergeometric_hrua(rk_state *state, long good, long bad, long sample); /* Triangular distribution */ extern double rk_triangular(rk_state *state, double left, double mode, double right); /* Logarithmic series distribution */ extern long rk_logseries(rk_state *state, double p); #ifdef __cplusplus } #endif #endif /* _RK_DISTR_ */