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

โœ Scribed by Zhishui Hu; Chun Su

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
219 KB
Volume
63
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

Let X 1 ; X 2 ; : : : ; be a sequence of i.i.d. random variables. X j ; j 6 n is called a near-maximum i X j falls within a distance of the maximum M n = max{X 1 ; : : : ; X n }. 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 S n (a)=S n are discussed, where S n (a) is the sum of near-maxima.

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