Distribution and expectation bounds on order statistics from possibly dependent variates

✍ Scribed by Nickos Papadatos

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 127 KB
• Volume: 54
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00014-1

✦ Synopsis

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 ∈ {1; 2; : : : ; n}), if the distribution F (j) of max{X k 1 ; : : : ; X k j } (resp. G (j) of min{X k 1 ; : : : ; X k j }) 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 F k:n of the kth order statistic X k: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 X k 1 ; : : : ; X k j is independent with a common marginal distribution F) are given.