Geodesic
A limit property of the geometric distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 404-408 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let random variables $X^{\ast}$, $X$ have discrete distributions on the nonnegative integers and let $$ \mathbf{P}\{X=k\}=c\sum^{\infty}_{j=k}\mathbf{P}\{X^{\ast}=j\},\qquad k=0,1,2,\dots, $$ with $c$ a proper constant. Repeated summations of this type are investigated. The limit distribution is geometric for a wide class of parent distributions.
Keywords: discrete distributions, partial-sums distributions, geometric distribution. 
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J. Macutek. A limit property of the geometric distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 404-408. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a15/

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