# A Rejection Technique for Sampling from T-Concave Distributions

Hörmann, Wolfgang (1994) A Rejection Technique for Sampling from T-Concave Distributions. Preprint Series / Department of Applied Statistics and Data Processing, 11. Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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## Abstract

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. (author's abstract)

Item Type: Paper © 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: ACM Transactions on Mathematical Software 21(2), 1995, pp. 182-193. http://doi.acm.org/10.1145/203082.203089 random number generation / rejection method / log-concave density / universal method MSC 65C10, 68C25 Departments > Finance, Accounting and Statistics > Statistics and Mathematics Repository Administrator 21 Dec 2005 13:50 22 Oct 2019 00:41 http://doi.acm.org/10.1145/203082.203089 https://epub.wu.ac.at/id/eprint/1028

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