On the Unimodality of High Convolutions of Discrete Distributions
نویسندگان
چکیده
It is shown that if { p j } is a discrete density function on the integers with support contained in {0 , 1 , ... , d }, and p 0 > 0, p 1 > 0, p d − 1 > 0, p d > 0, then there is an n 0 such that the n-fold convolution { p j } *n is unimodal for all n ≥ n 0 . Examples show that this result is nearly best possible, but weaker results are proved under less restrictive assumptions. On the Unimodality of High Convolutions of Discrete Distributions A. M. Odlyzko AT&T Bell Laboratories Murray Hill, New Jersey 07974 USA L. B. Richmond University of Waterloo Waterloo, Ontario Canada
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