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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 404–408 (Mi tvp119)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

A limit property of the geometric distribution

J. Macutek

Comenius University

Abstract: Let random variables $X^{\ast}$, $X$ have discrete distributions on the nonnegative integers and let
$$ \mathbf{P}\{X=k\}=c\sum^{\infty}_{j=k}\mathbf{P}\{X^{\ast}=j\},\qquad k=0,1,2,…, $$
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.

DOI: https://doi.org/10.4213/tvp119

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English version:
Theory of Probability and its Applications, 2006, 50:2, 316–319

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Received: 21.12.2001
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Citation: J. Macutek, “A limit property of the geometric distribution”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 404–408; Theory Probab. Appl., 50:2 (2006), 316–319

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Wimmer G., Macutek J., “New Integrated View at Partial-Sums Distributions”, Probastat `11: Proceedings of the Sixth International Conference on Probability and Statistics: Dedicated to Professor Lubomir Kubacek in Recognition of His Eightieth Birthday, Tatra Mountains Mathematical Publications, 51, eds. Volaufova J., Witkovsky V., Slovak Academy Sciences Mathematical Institute, 2012, 183–190  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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