Short Universal Generators Via Generalized Ratio-of-Uniforms Method

Josef Leydold


We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code.

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

Mathematics Subject Classification: 65C10 (Random Number Generation); 65U05 (Numerical methods in probability and statistics), 11K45 (Pseudo-random numbers, Monte Carlo methods)

General Terms: Algorithms

Key Words: non-uniform random variates, universal method, ratio-of-uniforms method, transformed density rejection, discrete distributions, continuous distributions, log-concave distributions, T-concave distributions

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