{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/7709"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/7709","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Heavy-Tailed Crack Distribution Families and Applications","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Chen, Jingjiao"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Bae, Taehan"],"committee_chairs":[],"committee_members":["Deng, DianLiang","Volodin, Andrei"],"year":2016,"date_issued":"2016-11","date_published":"2016-11","updated_at":"2026-07-24T04:03:39Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4539"],"render_values":[{"text":"https://doi.org/10.82465/4539","href":"https://doi.org/10.82465/4539","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/7709","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bae, Taehan"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Deng, DianLiang","Volodin, Andrei"]},{"key":"dc:creator","label":"Author","values":["Chen, Jingjiao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-19T22:44:04Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-19T22:44:04Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-11"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4539"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/7709"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Heavy-Tailed Crack Distribution Families and Applications"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bae, Taehan"],"dc:contributor.committeemember":["Deng, DianLiang","Volodin, Andrei"],"dc:creator":["Chen, Jingjiao"],"dc:date.accessioned":["2017-06-19T22:44:04Z"],"dc:date.available":["2017-06-19T22:44:04Z"],"dc:date.issued":["2016-11"],"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."],"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."],"dc:identifier.doi":["https://doi.org/10.82465/4539"],"dc:identifier.uri":["https://hdl.handle.net/10294/7709"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Heavy-Tailed Crack Distribution Families and Applications"],"dc:type":["master thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:39Z"}