Type-II Generalized Crack Distribution with Application to Heavy-Tailed Data Modeling

作     者：Bae, Taehan Volodin, Andrei 

作者机构：Univ Regina Math & Stat Regina SK Canada Xiamen Univ Technol Sino Canada Res Ctr Nonlinear Dynam & NoiseContro Xiamen Fujian Peoples R China 

出 版 物：《JOURNAL OF STATISTICAL THEORY AND PRACTICE》 (统计理论与实践杂志)

年 卷 期：2022年第16卷第3期

页      面：53-53页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Natural Science and Engineering Research Council of Canada NSERC [DDG-2019-06064] 

主　　题：Birnbaum-Saunders distribution Generalized crack distribution Extreme value theory EM algorithm Catastrophic loss 

摘      要：As an extension of the Birnbaum-Saunders distribution, the class of generalized crack (life-time) distributions has gained popularity in various applications including reliability theory and loss severity modeling. In particular for fat-tailed or heavy-tailed data sets, the generalized crack distribution family built on an appropriate base density functions, such as Student s t or generalized Gaussian densities, provides a sufficient level of flexibility to fit the empirical distribution effectively. In this paper, we introduce a further extension of the generalized crack distribution by including an additional shape parameter. We study some theoretical properties of the novel distribution family with a focus on its tail behavior. We further describe an application of the EM algorithm for model estimation with application to a real catastrophic loss data.