Limit theorems for the number and sum of near-maxima for medium tails

Zhishui Hu and Chun Su

Statistics & Probability Letters, 2003, vol. 63, issue 3, 229-237

Abstract: Let X1,X2,..., be a sequence of i.i.d. random variables. Xj, j[less-than-or-equals, slant]n is called a near-maximum iff Xj falls within a distance of the maximum Mn=max{X1,...,Xn}. In this paper, we focus on medium tailed distributions. A useful relationship on the number of near-maxima is built between general medium tailed and exponential distributions. Limit properties of the ratio Sn(a)/Sn are discussed, where Sn(a) is the sum of near-maxima.

Keywords: Near-maxima; Exponential; distribution; Thick; tail; Medium; tail (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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