Position of the maximum in a sequence with geometric distributionReport as inadecuate

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1 The John Knopfmacher Centre for Applicable Analysis and Number Theory Johannesburg

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 $1 ≤ d = on$.

Keywords : Mellin transforms generating functions geometric distribution.

Author: Margaret Archibald -

Source: https://hal.archives-ouvertes.fr/


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