Distribution and expectation bounds on order statistics from possibly dependent variates

Nickos Papadatos

Statistics & Probability Letters, 2001, vol. 54, issue 1, 21-31

Abstract: Let X1,X2,...,Xn be n random variables with an arbitrary n-variate distribution. We say that the X's are maximally (resp. minimally) stable of order j (j[set membership, variant]{1,2,...,n}), if the distribution F(j) of max{Xk1,...,Xkj} (resp. G(j) of min{Xk1,...,Xkj}) is the same, for any j-subset {k1,...,kj} of {1,2,...,n}. Under the assumption of maximal (resp. minimal) stability of order j, sharp upper (resp. lower) bounds are given for the distribution Fk:n of the kth order statistic Xk:n, in terms of F(j) (resp. G(j)), and the corresponding expectation bounds are derived. Moreover, some expectation bounds in the case of j-independent-F samples (i.e., when each j-tuple Xk1,...,Xkj is independent with a common marginal distribution F) are given.

Keywords: Dependent; random; variables; Bounds; on; order; statistics; Maximal; (minimal); stability; of; order; j; j-independent-F; samples (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (4)

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