Electronic Communications in Probability

Maxima of the cells of an equiprobable multinomial

Arup Bose, Amites Dasgupta, and Krishanu Maulik

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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.

Article information

Electron. Commun. Probab., Volume 12 (2007), paper no. 11, 93-105.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes 60F05: Central limit and other weak theorems
Secondary: 60F10: Large deviations

Random sequences triangular array maxima limit distribution

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Bose, Arup; Dasgupta, Amites; Maulik, Krishanu. Maxima of the cells of an equiprobable multinomial. Electron. Commun. Probab. 12 (2007), paper no. 11, 93--105. doi:10.1214/ECP.v12-1260. https://projecteuclid.org/euclid.ecp/1465224954

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