Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 1--9

CHARACTERIZATIONS OF THE LAPLACE AND RELATED DISTRIBUTIONS VIA GEOMETRIC COMPOUND

By

GWO DONG LIN, *Academia Sinica, Taiwan*

SUMMARY. Let F_{a , l }be the distribution with Linnik’s characteristic function f (t) = 1/(1+l |t|^{a} ), where l > 0 and a Î (0,2]. In this paper we first investigate the basic properties of F_{a , l }, including the self-decomposability and the existence of moments. Then using an elementary approach we prove two characterization theorems for F_{a , l }, which involve the stability of the geometric compound of a sequence of i.i.d. random variables.

*AMS (1991) subject classification.* Primary 62E10; secondary 60E10, 60E07.

*Key words and phrases.* Characterization of distribution, geometric compound and characteristic function.

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