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On Modeling the Earthquake Insurance Data via a New Member of the T-X Family
Computational Intelligence and Neuroscience ( IF 3.120 ) Pub Date : 2020-09-19 , DOI: 10.1155/2020/7631495
Zubair Ahmad 1 , Eisa Mahmoudi 1 , Omid Kharazmi 2
Affiliation  

Heavy-tailed distributions play an important role in modeling data in actuarial and financial sciences. In this article, a new method is suggested to define new distributions suitable for modeling data with a heavy right tail. The proposed method may be named as the Z-family of distributions. For illustrative purposes, a special submodel of the proposed family, called the Z-Weibull distribution, is considered in detail to model data with a heavy right tail. The method of maximum likelihood estimation is adopted to estimate the model parameters. A brief Monte Carlo simulation study for evaluating the maximum likelihood estimators is done. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is also done. An application of the Z-Weibull model to the earthquake insurance data is presented. Based on the analyses, we observed that the proposed distribution can be used quite effectively in modeling heavy-tailed data in insurance sciences and other related fields. Finally, Bayesian analysis and performance of Gibbs sampling for the earthquake data have also been carried out.

中文翻译:

通过TX系列的新成员对地震保险数据进行建模

重尾分布在精算和金融科学中的数据建模中起着重要作用。在本文中,提出了一种新方法来定义适用于对右尾巴较重的数据进行建模的新分布。所提出的方法可以被称为分布的Z族。为了说明的目的,将详细考虑所提议族的一个特殊子模型,称为Z-Weibull分布,以对右尾巴较重的数据进行建模。采用最大似然估计法对模型参数进行估计。完成了用于评估最大似然估计器的简短蒙特卡罗模拟研究。此外,还计算了一些精算指标,例如风险值和尾部风险值。还基于这些精算方法进行了仿真研究。介绍了Z-Weibull模型在地震保险数据中的应用。基于分析,我们观察到建议的分布可以非常有效地用于保险科学和其他相关领域的重尾数据建模。最后,还对地震数据进行了贝叶斯分析和吉布斯采样的性能。
更新日期:2020-09-20
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