Distribution and expectation bounds on order statistics from possibly dependent variates
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.
Year of publication: |
2001
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Authors: | Papadatos, Nickos |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 54.2001, 1, p. 21-31
|
Publisher: |
Elsevier |
Keywords: | Dependent random variables Bounds on order statistics Maximal (minimal) stability of order j j-independent-F samples |
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