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February, 1985 On the Unimodality of High Convolutions of Discrete Distributions
A. M. Odlyzko, L. B. Richmond
Ann. Probab. 13(1): 299-306 (February, 1985). DOI: 10.1214/aop/1176993082


It is shown that if $\{p_j\}$ is a discrete density function on the integers with support contained in $\{0, 1, \cdots, d\}$, 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 $\{p_j\}^{\ast_n}$ is unimodal for all $n \geq n_0$. Examples show that this result is nearly best possible, but weaker results are proved under less restrictive assumptions.


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A. M. Odlyzko. L. B. Richmond. "On the Unimodality of High Convolutions of Discrete Distributions." Ann. Probab. 13 (1) 299 - 306, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0561.60021
MathSciNet: MR770644
Digital Object Identifier: 10.1214/aop/1176993082

Primary: 60E05

Keywords: discrete distributions , Unimodality

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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