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 $F$.
Citation
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
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