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- W2004187725 abstract "Consider {Xj, j ⩾ 1}, a sequence of i.i.d., positive, integer-valued random variables. Let Kn denote the number of the integer j ∈ {1,2,…,n} for which Xj = max1⩽m⩽n Xm. In this paper we prove that limn→∞ EKn = 1 if and only if Kn converges in probability to one, if and only if limn→∞ P(X1=n)/P(X1⩾n)=0 and prove that Kn converges almost surely to one, if and only if ∑n=1∞(P(X1 = n)P(X1⩾n))2 < ∞. Some of the results were shown by Baryshnikov et al. (1995) and Brands et al. (1994)." @default.
- W2004187725 created "2016-06-24" @default.
- W2004187725 creator A5019013453 @default.
- W2004187725 date "1997-05-01" @default.
- W2004187725 modified "2023-09-23" @default.
- W2004187725 title "A note on the number of maxima in a discrete sample" @default.
- W2004187725 cites W1990522598 @default.
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- W2004187725 doi "https://doi.org/10.1016/s0167-7152(96)00150-2" @default.
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