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Characterizations of the Laplace and Related Distributions via Geometric Compound

Gwo Dong Lin
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 56, No. 1 (Feb., 1994), pp. 1-9
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050963
Page Count: 9
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Characterizations of the Laplace and Related Distributions via Geometric Compound
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Abstract

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

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