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TitleApproximate moments of extremes
Publication TypeJournal Article
Year of Publication2015
AuthorsWithers, C.S., and Nadarajah S.
JournalJournal of Inequalities and Applications
Date Published2015
ISSN10255834 (ISSN)
AbstractLet Mn,i be the ith largest of a random sample of size n from a cumulative distribution function F on R=(−∞,∞). Fix r≥1 and let Mn=(Mn,1,...Mn,r)’. If there exist bnand cn> 0 such that as (Formula presented.)G say, a non-degenerate distribution, then as (Formula presented.), where for (Formula presented.) has joint probability density function exp(−zr)on 01<⋯r<∞ and 1r is the r-vector of ones. The moments of Y are given for the three possible forms of G. First approximations for the moments of Mn are obtained when these exist. © 2015, Withers and Nadarajah.

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