A note on the number of records near the maximum

Yun Li

Statistics & Probability Letters, 1999, vol. 43, issue 2, 153-158

Abstract: Let {Xn,n[greater-or-equal, slanted]1} be a sequence of independent identically distributed random variables with the continuous distribution function F(x). Let Kn(a) denote the number of values j[set membership, variant]{1,2,...,n} for which Xj[set membership, variant](Mn-a,Mn], where Mn=max{X1,...,Xn} and a is a positive constant. In this paper we prove that limn-->[infinity] E(Kn(a))=1 if and only if Kn(a) converges in probability to one, if and only if when F(x) has a thick tail. Furthermore, we will give a necessary and sufficient condition for

Keywords: Record; near; the; maximum; Almost; sure; convergence (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (10)

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