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Position of the maximum in a sequence with geometric distribution

Abstract : 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 $1 ≤ d = o(n)$.
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Margaret Archibald. Position of the maximum in a sequence with geometric distribution. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.11-16. ⟨hal-01184039⟩

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