Heavy-Tailed Crack Distribution Families and Applications

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.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2016

Author dc:creator

• Chen, Jingjiao

Advisor dc:contributor.advisor

• Bae, Taehan

Committee members dc:contributor.committeemember

• Deng, DianLiang
• Volodin, Andrei

Language dc:language.iso

en

DOI

https://doi.org/10.82465/4539

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/7709