EXPONENTIAL MIXTURE REPRESENTATION OF GEOMETRIC STABLE DISTRIBUTIONS

TOMASZ J. KOZUBOWSKI

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

(Received February 9, 1998; revised July 3, 1998)

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.

Key words and phrases: Heavy-tail distribution, Linnik distribution, Mittag-Leffler distribution, random summation, stable distribution.

——–