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A range reduction method for generating discrete random variables

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  • Shmerling, Efraim

Abstract

A new general method for generating discrete random variables is presented. The method is based on reducing the problem of generating a discrete random variable with an extremely large range to that of generating a random variable with a small range consisting of a few possible values (i.e. range reduction). The validity of the method presented is proved, and its performance is examined and compared to the performance of previously developed general methods. A random number generator for geometric variables of order r based on the range reduction method is given as an illustration of its advantages.

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  • Shmerling, Efraim, 2013. "A range reduction method for generating discrete random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1094-1099.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1094-1099
    DOI: 10.1016/j.spl.2013.01.002
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    1. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
    2. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2004. "Fast Generation of Discrete Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i03).
    3. J. Cole Smith & Sheldon H. Jacobson, 2005. "An Analysis of the Alias Method for Discrete Random-Variate Generation," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 321-327, August.
    4. Sigeo Aki & Katuomi Hirano, 2007. "On the Waiting Time for the First Success Run," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 597-602, September.
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    Cited by:

    1. Aletti, Giacomo, 2018. "Generation of discrete random variables in scalable frameworks," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 99-106.

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