2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 1116
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. 1116 
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