Geodesic
Position of the maximum in a sequence with geometric distribution
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005).

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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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     author = {Archibald, Margaret},
     title = {Position of the maximum in a sequence with geometric distribution},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms},
     year = {2005},
     doi = {10.46298/dmtcs.3367},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3367/}
}
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Archibald, Margaret. Position of the maximum in a sequence with geometric distribution. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms (2005). doi : 10.46298/dmtcs.3367. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3367/

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