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dc.contributor.authorLiang, Jiaxi
dc.date.accessioned2011-04-29 17:25:43 (GMT)
dc.date.available2011-04-29 17:25:43 (GMT)
dc.date.issued2011-04-29T17:25:43Z
dc.date.submitted2011
dc.identifier.urihttp://hdl.handle.net/10012/5886
dc.description.abstractIn this thesis, we are interested in using the Padé approximants and asymptotic series to approximate the density functions of the stable distributions. The paper specifically discusses the selection of the optimal degree and central point of Padé approximants as well as how to connect the Padé approximants and asymptotic series as a piecewise function. Based on such approximation, a computational algorithm is developed to estimate the maximum likelihood estimator with confidence interval of the parameters, using quasi-Newton method. Simulations are conducted to evaluate the performance of this algorithm, and comparisons are made to Nolan's integral method to show that the method introduced in the thesis is fast and reliable in approximation and estimation.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectStable distributionen
dc.subjectPadé approximantsen
dc.titleApproximating stable densities with Padé approximants and asymptotic seriesen
dc.typeMaster Thesisen
dc.pendingfalseen
dc.subject.programStatisticsen
uws-etd.degree.departmentStatistics and Actuarial Scienceen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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