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 distributionConference paper
Authors: Margaret Archibald 1
NULL
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).