On the Unimodality of High Convolutions of Discrete Distributions
Odlyzko, A. M. ; Richmond, L. B.
Ann. Probab., Tome 13 (1985) no. 4, p. 299-306 / Harvested from Project Euclid
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.
Publié le : 1985-02-14
Classification:  Unimodality,  discrete distributions,  60E05
@article{1176993082,
     author = {Odlyzko, A. M. and Richmond, L. B.},
     title = {On the Unimodality of High Convolutions of Discrete Distributions},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 299-306},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993082}
}
Odlyzko, A. M.; Richmond, L. B. On the Unimodality of High Convolutions of Discrete Distributions. Ann. Probab., Tome 13 (1985) no. 4, pp.  299-306. http://gdmltest.u-ga.fr/item/1176993082/