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Methods for generating random variates with Polya characteristic functions

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  • Devroye, Luc

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.

Suggested Citation

  • Devroye, Luc, 1984. "Methods for generating random variates with Polya characteristic functions," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 257-261, October.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:5:p:257-261
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    Cited by:

    1. Devroye, Luc, 1989. "On random variate generation when only moments or Fourier coefficients are known," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 31(1), pages 71-89.
    2. Luc Devroye & Lancelot James, 2014. "On simulation and properties of the stable law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 307-343, August.

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