A characterization of geometric distributions by distributional properties of order statistics
- 1 October 1976
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1976 (4) , 232-234
- https://doi.org/10.1080/03461238.1976.10405619
Abstract
Let X 1, X 2 be independent identically distributed positive integer valued random variables. H the X i 's have a geometric distribution, then the conditional distribution of R = max(X 1, X 2)-min(X 1, X 2), given R > 0, is the same as the distribution of X 1. This property is shown to characterize the geometric distribution.Keywords
This publication has 1 reference indexed in Scilit:
- A Characterization Based on the Absolute Difference of Two I. I. D. Random VariablesThe Annals of Mathematical Statistics, 1970