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A Universal Generator for Bivariate Log-Concave Distributions

Hörmann, Wolfgang (1995) A Universal Generator for Bivariate Log-Concave Distributions. Preprint Series / Department of Applied Statistics and Data Processing, 13. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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Abstract

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. (author's abstract)

Item Type: Paper
Keywords: random number generation / rejection method / bivariate log-concave distributions / universal generator
Classification Codes: MSC 65C10
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 10 Jul 2006 08:26
Last Modified: 16 Feb 2015 11:56
URI: http://epub.wu.ac.at/id/eprint/1044

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