On the normal uniform local domain of attraction for intermediate order statistics

Johan Segers

Statistics & Probability Letters, 2001, vol. 53, issue 4, 409-413

Abstract: Let X1,X2,... be independent observations from the absolutely continuous distribution function F with quantile function Q. The density of the normalized order statistic Xn-kn+1:n converges locally uniformly to the standard normal density for any sequence kn with kn-->[infinity] and kn/n-->0 if and only if log (d/dx)Q(1-1/x) is slowly oscillating.

Keywords: Intermediate; order; statistics; Domain; of; attraction; Tail; quantile; density; Slowly; oscillating; function (search for similar items in EconPapers)
Date: 2001
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