Two Characterizations of the Geometric Distribution
- 1 March 1974
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 69 (345) , 267
- https://doi.org/10.2307/2285541
Abstract
Let X 1, …, Xn, n ≥ 2 be n i.i.d. r.v.'s, each having a geometric distribution, and let Y 1 ≤ … ≤ Yn be the corresponding order statistics. Write Z = Σn i-2 (Y i − Y 1). Then it is well known that Y 1 and Z are independent. In this article, we show that a very weak form of this property is a characterizing property of the geometric distribution. Other characterizations of the geometric distribution are also obtained by similar properties.Keywords
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