DMTCS

2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 11-16


author: M. Archibald
title: Position of the maximum in a sequence with geometric distribution
keywords: Mellin transforms, generating functions, 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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reference: M. Archibald (2005), Position of the maximum in a sequence with geometric distribution, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 11-16
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