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A note on the number of maxima in a discrete sample

✍ Scribed by Yongcheng Qi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
163 KB
Volume
33
Category
Article
ISSN
0167-7152

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✦ Synopsis

Consider {Xj, j>~ 1 }, a sequence of i.i.d., positive, integer-valued random variables. Let K, denote the number of the integer j ~ {1,2,... ,n} for which Xj = maxl~m~~n)=0 and prove that Kn converges almost surely to one, if and only if ~t(P(Xl = n)/P(X1 >~n)) 2 < c~. Some of the results were shown by Baryshnikov et al. (1995) and Brands et al. (1994).

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