Geodesic
A limit property of the geometric distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 404-408

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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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     author = {J. Macutek},
     title = {A limit property of the geometric distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {404--408},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a15/}
}
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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/