A Rejection Technique for sampling from T-Concave Distributions

Wolfgang Hörmann


A rejection algorithm - called transformed density rejection - that uses a new method for constructing simple hat functions for an unimodal, bounded density $f$ is introduced. It is based on the idea to transform $f$ with a suitable transformation $T$ such that $T(f(x))$ is concave. $f$ is then called $T$-concave and tangents of $T(f(x))$ in the mode and in a point on the left and right side are used to construct a hat function with table-mountain shape. It is possible to give conditions for the optimal choice of these points of contact. With $T=-1/\sqrt{x}$ the method can be used to construct a universal algorithm that is applicable to a large class of unimodal distributions including the normal, beta, gamma and t-distribution.

Mathematics Subject Classification: 65C10 (Random Number Generation), 68C25

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

General Terms: Algorithms

Key Words: random number generation, rejection method, log-concave density, universal method

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© ACM, (1995). 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. 21(2), 182-193. http://doi.acm.org/10.1145/203082.203089