Illustration of some moment identities for order statistics

Kenneth Lange

Statistics & Probability Letters, 1996, vol. 27, issue 1, 91-98

Abstract: This paper discusses some identities for the marginal distribution functions and marginal moments of the order statistics X(1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] X(n) of n random variables X1, ..., Xn. These identities express the distribution function or moments of X(1) as linear combinations of the distribution functions or moments of minima or maxima of subsets of the Xi. Two applications to waiting time problems in urn sampling illustrate the value of the moment identities. These applications rely on embedding the urn models in Poisson and uniform stochastic processes.

Keywords: Bonferroni; inequalities; Urn; model; Probabilistic; embedding (search for similar items in EconPapers)
Date: 1996
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