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Exponential Mixture Representation of Geometric Stable Distributions

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Abstract

We show that every strictly geometric stable (GS) random variable can be represented as a product of an exponentially distributed random variable and an independent random variable with an explicit density and distribution function. An immediate application of the representation is a straightforward simulation method of GS random variables. Our result generalizes previous representations for the special cases of Mittag-Leffler and symmetric Linnik distributions.

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Authors and Affiliations

  1. Department of Mathematics, The University of Tennessee at Chattanooga, Chattanooga, TN, 37403, U.S.A.

    Tomasz J. Kozubowski

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  1. Tomasz J. Kozubowski
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Kozubowski, T.J. Exponential Mixture Representation of Geometric Stable Distributions. Annals of the Institute of Statistical Mathematics 52, 231–238 (2000). https://doi.org/10.1023/A:1004157620644

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