NDLI: Algorithm 802: an automatic generator for bivariate log-concave distributions

Content Provider	ACM Digital Library
Author	Hörmann, Wolfgang
Copyright Year	2000
Abstract	Different automatic (also called universal or black-box) methods have been suggested to sample from univariate log-concave distributions. Our new automatic 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 points that are rejected by the rejection algorithm can be used as additional points of contact. The article describes the details how this main idea can be used to construct Algorithm ALC2D that can generate random pairs from all bivariate log-concave distributions with known domain, computable density, and computable partial derivatives.
Starting Page	201
Ending Page	219
Page Count	19
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/347837.347908
Volume Number	26
Issue Number	1
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2000-03-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Automatic generator Bivariate log-concave distributions Rejection method Universal generator
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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