Heavy-Tailed Crack Distribution Families and Applications

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dc.contributor.advisor Bae, Taehan
dc.contributor.author Chen, Jingjiao
dc.date.accessioned 2017-06-19T22:44:04Z
dc.date.available 2017-06-19T22:44:04Z
dc.date.issued 2016-11
dc.identifier.uri http://hdl.handle.net/10294/7709
dc.description A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. viii, 76 p. en_US
dc.description.abstract The heavy-tailedness and right-skewness are two typical features of loss data resulting from catastrophic natural phenomena such as severe weather events and earthquakes. In this thesis, we consider a new class of heavy-tailed crack distribution families as an extension of the three-parameter Gaussian crack distribution (Volodin and Dzhungurova, 2000) of which the right tail lacks exibility to t heavy-tailed observations. Several key distributional properties of the generalized crack distribution (Leiva et al., 2010, Bae and Volodin, 2014) are discussed with a particular emphasis on the tail behavior. The theoretical tail relationships between the auxiliary distribution and the resulting crack distribution are studied relying on the classical theories of extreme values and regular variation. Moreover, we discuss the asymptotic behavior of the hazard rate function of the generalized crack distribution. Student's t crack, Laplace crack, the generalized Gaussian crack distributions are proposed as illustrative examples for theorems and applications. A few model tting exercises are carried out based on both simulated and real catastrophic loss data sets. For a model tting approach, the maximum likelihood method is used with the pro le log-likelihood algorithm. The tting results show that the heavy-tailed crack distribution with an appropriate choice of auxiliary density function outperforms well-known parametric models, such as Log-normal, Pareto type II and Weibull distributions, which are popular in modeling positively skewed and heavy-tailed extreme data sets. en_US
dc.language.iso en en_US
dc.publisher Faculty of Graduate Studies and Research, University of Regina en_US
dc.title Heavy-Tailed Crack Distribution Families and Applications en_US
dc.type Thesis en
dc.description.authorstatus Student en
dc.description.peerreview yes en
thesis.degree.name Master of Science (MSc) en_US
thesis.degree.level Master's en
thesis.degree.discipline Statistics en_US
thesis.degree.grantor University of Regina en
thesis.degree.department Department of Mathematics and Statistics en_US
dc.contributor.committeemember Deng, DianLiang
dc.contributor.committeemember Volodin, Andrei
dc.identifier.tcnumber TC-SRU-7709
dc.identifier.thesisurl http://ourspace.uregina.ca/bitstream/handle/10294/7709/Chen_Jingjiao_200355098_MSC_STAT_Spring2017.pdf

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