Margaret Archibald

Position of the maximum in a sequence with geometric distribution
dmtcs:3367 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms

https://doi.org/10.46298/dmtcs.3367
Position of the maximum in a sequence with geometric distribution
Authors: Margaret Archibald ^{1}
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Margaret Archibald
1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]
As a sequel to [arch04], the position of the maximum in a geometrically distributed sample is investigated. Samples of length n are considered, where the maximum is required to be in the first d positions. The probability that the maximum occurs in the first $d$ positions is sought for $d$ dependent on n (as opposed to d fixed in [arch04]). Two scenarios are discussed. The first is when $d=αn$ for $0 < α ≤ 1$, where Mellin transforms are used to obtain the asymptotic results. The second is when $1 ≤ d = o(n)$.