On the number of maxima in a discrete sample

J. J. A. M. Brands, F. W. Steutel and R. J. G. Wilms

Statistics & Probability Letters, 1994, vol. 20, issue 3, 209-217

Abstract: Let Mn = max(N1,..., Nn), where N1, N2, ... are i.i.d., positive, integer-valued r.v.'s. We are interested in Kn, the number of values of j [epsilon] {1, 2, ..., n} for which Nj = Mn, especially for large values of n. There is strong evidence that Kn either tends to one or to infinity, or diverges in distribution as n tends to infinity. An interesting example of the latter type occurs when N1 has a geometric distribution. There is an application of results on Kn to the behaviour of the fractional parts of sample maxima from non-integer populations.

Keywords: Extreme; values; in; discrete; samples; Fractional; parts; of; maxima; Coin; tossing (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (13)

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