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2007 Maxima of the cells of an equiprobable multinomial
Arup Bose, Amites Dasgupta, Krishanu Maulik
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Electron. Commun. Probab. 12: 93-105 (2007). DOI: 10.1214/ECP.v12-1260

Abstract

Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a suitable centering and scaling converges to the Gumbel distribution. While results are available for maxima of triangular arrays of independent random variables with certain types of distribution, such results in a dependent setup is new. We also prove that the maxima of a triangular sequence of appropriate Binomial random variables have the same limit distribution. An auxiliary large deviation result for multinomial distribution with increasing number of equiprobable cells may also be of independent interest.

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Arup Bose. Amites Dasgupta. Krishanu Maulik. "Maxima of the cells of an equiprobable multinomial." Electron. Commun. Probab. 12 93 - 105, 2007. https://doi.org/10.1214/ECP.v12-1260

Information

Accepted: 24 April 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1141.60031
MathSciNet: MR2300219
Digital Object Identifier: 10.1214/ECP.v12-1260

Subjects:
Primary: 60F05, 60G70
Secondary: 60F10

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