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Position of the maximum in a sequence with geometric distribution

By Margaret Archibald

Abstract

As a sequel to [1], 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 [1]). 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)

Topics: Mellin transforms, generating functions, geometric distribution
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.381.4178
Provided by: CiteSeerX
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