Maxima of Dirichlet and triangular arrays of gamma variables
Probability
2009-03-06 v1 Statistics Theory
Statistics Theory
Abstract
Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power transformation. Depending on the parameter combinations, we obtain both Gumbel and non-Gumbel limits. The weak limits for maximum of the coordinates of certain Dirichlet vectors of increasing dimension are also obtained using the gamma representation.
Cite
@article{arxiv.0803.3518,
title = {Maxima of Dirichlet and triangular arrays of gamma variables},
author = {Arup Bose and Amites Dasgupta and Krishanu Maulik},
journal= {arXiv preprint arXiv:0803.3518},
year = {2009}
}