{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Dynamic Elliptical Distributions","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree"},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/78204"},{"label":"dc.language.iso","value":"en_US"},{"label":"dcterms.abstract","value":"Current multivariate distributions have a static covariance structure. This implies that the levels of covariance between components of a system are the same during \u201cnormal\u201d times and tail events. Many real world systems do not exhibit constant covariance between components across time. There are currently two primary ways to deal with this issue. The first is to take a heterogeneous approach by fitting a multivariate distribution to \u201cnormal\u201d data and use extreme value theory to analyze tail data. The second approach is to fit marginal distributions to the components and use them to construct a copula. We show that there are drawbacks to each of these techniques. We suggest a more homogenous approach through the development of a new class of multivariate distributions called dynamic elliptical distributions. Dynamic elliptical distributions have a covariance matrix whose entries are functions. This dynamic covariance matrix acts as a local metric on the sample space, which allows the degree of covariance to change as one moves from the center of the distribution to its tails. We develop sampling and fitting methods for dynamic elliptical distributions and show the role they play in information geometry. More specifically we derive the general information geometry of elliptical distributions and show conditions under which these smooth manifolds become Einstein manifolds. Finally we show that any dynamic elliptical distribution can be regarded as a submanifold on a manifold of elliptical distributions."},{"label":"dcterms.available","value":"2018-03-22T22:39:18Z"},{"label":"dcterms.contributor","value":"Mullhaupt, Andrew P"},{"label":"dcterms.creator","value":"Tiano, Michael John"},{"label":"dcterms.dateAccepted","value":"2018-03-22T22:39:18Z"},{"label":"dcterms.dateSubmitted","value":"2018-03-22T22:39:18Z"},{"label":"dcterms.description","value":"Department of Applied Mathematics and Statistics."},{"label":"dcterms.extent","value":"101 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/78204"},{"label":"dcterms.issued","value":"2017-08-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2018-03-22T22:39:18Z (GMT). No. of bitstreams: 1\nTiano_grad.sunysb_0771E_13281.pdf: 1319519 bytes, checksum: fc95e7f52562f1bdaeb9b25d5d9cffc6 (MD5)\n  Previous issue date: 2017-08-01"},{"label":"dcterms.subject","value":"Applied mathematics"},{"label":"dcterms.title","value":"Dynamic Elliptical Distributions"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/15%2F40%2F85%2F154085018097906010115695021543527942291/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/15%2F40%2F85%2F154085018097906010115695021543527942291","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}