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 Fa , 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 Fa , l , including the self-decomposability and the existence of moments. Then using an elementary approach we prove two characterization theorems for Fa , 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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