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May, 1975 Characterization of Distributions by Sets of Moments of Order Statistics
Barry C. Arnold, Glen Meeden
Ann. Statist. 3(3): 754-758 (May, 1975). DOI: 10.1214/aos/1176343141

Abstract

It is known that the set $M = \{\mu_{r,n} : r = 1, 2, \cdots, n; n = 1, 2, 3, \cdots\}$ of expectations of order statistics of samples from a distribution $F$ completely determines $F$ (see, for example, Hoeffding (1953)). In addition Chan (1967), Konheim (1971) and Pollak (1973) have shown that certain subsets of $M$ determine $F$. In this note conditions are derived which are sufficient for a proper subset of $M$ to determine $F$.

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Barry C. Arnold. Glen Meeden. "Characterization of Distributions by Sets of Moments of Order Statistics." Ann. Statist. 3 (3) 754 - 758, May, 1975. https://doi.org/10.1214/aos/1176343141

Information

Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0308.62006
MathSciNet: MR378264
Digital Object Identifier: 10.1214/aos/1176343141

Subjects:
Primary: 62E10
Secondary: 62 630

Keywords: characterization , moments of order statistics

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 3 • May, 1975
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