Abstract
This paper discusses some identities for the marginal distribution functions and marginal moments of the order statistics X (1) ⩽ … ⩽ X ( n) of n random variables X 1, …, X n . 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 X i . 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.
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