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On multivariate unimodal distributions

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Title: On multivariate unimodal distributions
Author: Dai, Tao
Degree Master of Science - MSc
Program Statistics
Copyright Date: 1989
Abstract: In this thesis, Kanter's representation of multivariate unimodal distributions is shown equivalent to the usual mixture of uniform distributions on symmetric, compact and convex sets. Kanter's idea is utilized in several contexts by viewing multivariate distributions as mixtures of uniform distributions on sets of various shapes. This provides a unifying viewpoint of what is in the literature and gives some important new classes of multivariate unimodal distributions. The closure properties of these new classes under convolution, marginality and weak convergence, etc. and their relationships with other notions of multivariate unimodality are discussed. Some interesting examples and their 2- or 3-dimensional pictures are presented.
URI: http://hdl.handle.net/2429/27411
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

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