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dc.contributor.advisorSubasi, Munevver Mine
dc.contributor.authorAlharbi, Majed Ghazi S
dc.date.accessioned2018-01-18T18:46:32Z
dc.date.available2018-01-18T18:46:32Z
dc.date.created2017-12
dc.date.issued2017-12
dc.date.submittedDecember 2017
dc.identifier.urihttp://hdl.handle.net/11141/2288
dc.descriptionThesis (Ph.D.) - Florida Institute of Technology, 2017en_US
dc.description.abstractThe 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.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen_US
dc.rightsCopyright held by author.en_US
dc.titleOn Logconcavity of Multivariate Discrete Distributionsen_US
dc.typeDissertationen_US
dc.date.updated2018-01-08T20:07:03Z
thesis.degree.nameDoctorate of Philosophy in Operations Researchen_US
thesis.degree.levelDoctoralen_US
thesis.degree.disciplineOperations Researchen_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.grantorFlorida Institute of Technologyen_US
dc.type.materialtext


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