On Logconcavity of Multivariate Discrete Distributions
Alharbi, Majed Ghazi S
MetadataShow full item record
The contribution of this dissertation to the literature is twofold. First, we use a geometric perspective to present all possible subdivisions of R³ into tetrahedra with disjoint interiors and adopt a combinatorial approach to obtain a special subdivision of Rⁿ into simplices with disjoint interiors, where two simplices are called neighbors if they share a common facet. We then use the neighborhood relationship of the simplices in each subdivision to fully describe the sufficient conditions for the strong unimodality/logconcavity of the trivariate discrete distributions and further extend these results to present a new sufcient condition for the strong unimodality/logconcavity of multivariate discrete distributions defined on Zⁿ. We show that the multivariate P´olya-Eggenberger distribution, multivariate Poisson distribution, and multivariate Ewens distribution are strongly unimodal, and hence logconcave.