On strong unimodality of multivariate discrete distributions

A discrete function f defined on Zⁿ is said to be logconcave if for , , . A more restrictive notion is strong unimodality. Following Barndorff-Nielsen [O. Barndorff-Nielsen, Unimodality and exponential families, Commun. Statist. 1 (1973) 189-216] a discrete function is called strongly unimodal if there exists a convex function such that  if . In this paper sufficient conditions that ensure the strong unimodality of a multivariate discrete distribution, are given. Examples of strongly unimodal multivariate discrete distributions are presented.