The number and sum of near-maxima for thin-tailed populations

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Abstract

A near-maximum is an observation which falls within a distance a of the maximum observation in an i.i.d. sample of size n. The asymptotic behaviour of the number K-n(a) of near-maxima is known for the cases where the right extremity of the population distribution function is finite, and where it is infinite and the right hand tail is exponentially small, or fatter than exponential. This paper completes the picture for thin tails, i.e., tails which decay faster than exponential. Limit theorems are derived and used to find the large-sample behaviour of the sum of near-maxima.
Original languageEnglish
Pages (from-to)1100-1116
JournalAdvances in Applied Probability
Volume32
Publication statusPublished - 2000

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