Methods for generating random variates with Polya characteristic functions

Luc Devroye

Statistics & Probability Letters, 1984, vol. 2, issue 5, 257-261

Abstract: Polya has shown that real even continuous functions that are convex on (0,[infinity]), for 1 t = 0, and decreasing to 0 as t --> [infinity] are characteristic functions. Dugué and Girault (1955) have shown that the corresponding random variables are distributed as Y/Z where Y is a random variable with density (2[pi])-1(sin(x/2)/(x/2))2, and Z is independent of Y and has distribution function 1 - [phi] + t[phi]', t > 0. This property allows us to develop fast algorithms for this class of distributions. This is illustrated for the symmetric stable distribution, Linnik's distribution and a few other distributions. We pay special attention to the generation of Y.

Keywords: random; variate; generation; Polya; characteristic; function; symmetric; stable; distribution; convexity; algorithms (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (2)

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