A Universal Generator for Bivariate Log-Concave Distributions

Wolfgang Hörmann


Different universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that a point that is rejected by the rejection algorithm is used as additional point of contact until the maximal number of points of contact is reached. The paper describes the details how this main idea can be used to construct Algorithm ULC2D that can generate random pairs from bivariate log-concave distribution with a computable density.

Mathematics Subject Classification: 65C10 (Random Number Generation)

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

General Terms: Algorithms

Key Words: random number generation, rejection method, bivariate log-concave distributions, universal generator

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© ACM, (2000). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Trans. Math. Softw. 26(1), 201 - 219. http://doi.acm.org/10.1145/347837.347908