Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Rebecca Killick, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: George Marsaglia, Wai Wan Tsang
Title: The Ziggurat Method for Generating Random Variables
Abstract: We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers ki, and reals wi. Some 99% of the time, the required x is produced by: Generate a random 32-bit integer j and let i be the index formed from the rightmost 8 bits of j. If j < k, return x = j x wi.

We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for settting up the necessary tables.

Page views:: 57425. Submitted: 2000-04-15. Published: 2000-10-02.
Paper: The Ziggurat Method for Generating Random Variables     Download PDF (Downloads: 46880)
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rnorrexp.c: C code for the ziggurat method for RNOR and REXP Download (Downloads: 14952; 3KB)
DOI: 10.18637/jss.v005.i08

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Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.