# The transformed rejection method for generating Poisson random variables

Hörmann, Wolfgang (1992) The transformed rejection method for generating Poisson random variables. Preprint Series / Department of Applied Statistics and Data Processing, 2. Institut für Statistik und Mathematik, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.

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## Abstract

The transformed rejection method, a combination of the inversion and the rejection method, which is used to generate non-uniform random numbers from a variety of continuous distributions can be applied to discrete distributions as well. For the Poisson distribution a short and simple algorithm is obtained which is well suited for large values of the Poisson parameter $\mu$, even when $\mu$ may vary from call to call. The average number of uniform deviates required is lower than for any of the known uniformly fast algorithms. Timings for a C implementation show that the algorithm needs only half of the code but is - for $\mu$ not too small - at least as fast as the current state-of-the-art algorithms. (author's abstract)

Item Type: Paper In: Insurance: Mathematics and Economics 12, pp. 39-45, 1993 rejection method / inversion / decomposition / Poisson variate generation / uniformly fast algorithm MSC 65C10, CR G.3 Departments > Finance, Accounting and Statistics > Statistics and Mathematics Repository Administrator 03 May 2004 19:19 22 Oct 2019 00:41 https://epub.wu.ac.at/id/eprint/352

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