AISM 52, 231-238

## 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.

**Source**
( TeX , DVI )