A Characterization of Geometric Distributions by Distributional Properties of Order Statistics.

摘要

Let X1, X2 be independent identically distributed positive integer valued random variables. If the Xi's have a geometric distribution, then the conditional distribution of R = max(X1, X2)-min(X1, X2), given R>O, is the same as the distribution of X1. This property is shown to characterize the geometric distribution. (Author)