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Illustration of some moment identities for order statistics

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  • Lange, Kenneth

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.

Suggested Citation

  • Lange, Kenneth, 1996. "Illustration of some moment identities for order statistics," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 91-98, March.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:1:p:91-98
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    References listed on IDEAS

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    1. N. Balakrishnan & S. Bendre & H. Malik, 1992. "General relations and identities for order statistics from non-independent non-identical variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 177-183, March.
    2. N. Salakbishnan, 1988. "Recurrence relations for order statistics from n independent and non-identically distributed random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 273-277, June.
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