Mixtures of Shifted Asymmetric Laplace Distributions

dc.contributor.advisorMcNicholas, Paul
dc.contributor.advisorBrowne, Ryan
dc.contributor.authorFranczak, Brian
dc.date.accessioned2014-04-21T13:53:06Z
dc.date.available2014-04-21T13:53:06Z
dc.date.copyright2014-03
dc.date.created2014-03-04
dc.date.issued2014-04-21
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameDoctor of Philosophyen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractIn this thesis we introduce a mixture of shifted asymmetric Laplace (SAL) distributions for model-based clustering and classification. The mixture of SAL distributions allows for the parameterization of skewness as well as location and scale. Furthermore, we extend the general SAL mixture by decomposing the component scale matrices; this results in two families of SAL mixture models and a generalization of the multivariate SAL density. In developing these models we review and utilize several facets of model-based clustering. Specifically, to estimate the parameters of our mixture models we use the well-known expectation-maximization algorithm, to choose the best fitting mixture model we consider both the Bayesian information criterion and integrated completed likelihood, and to evaluate classification performance we use the adjusted Rand index. Both simulated and real data are used to demonstrate our models.en_US
dc.identifier.urihttp://hdl.handle.net/10214/8006
dc.language.isoenen_US
dc.publisherUniversity of Guelphen_US
dc.rights.licenseAll items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectfinite mixture modelsen_US
dc.subjectmodel-based clusteringen_US
dc.subjectmultivariate analysisen_US
dc.subjectasymmetric Laplaceen_US
dc.titleMixtures of Shifted Asymmetric Laplace Distributionsen_US
dc.typeThesisen_US

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