Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran.
Department of Statistics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Comput Intell Neurosci. 2020 Sep 19;2020:7631495. doi: 10.1155/2020/7631495. eCollection 2020.
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.
重尾分布在精算学和金融科学中的数据建模中起着重要作用。本文提出了一种新的方法来定义新的分布，这些分布适合于对具有重右尾的数据进行建模。所提出的方法可以命名为 Z 族分布。为了说明问题，详细考虑了所提出族的一个特殊子模型，称为 Z-Weibull 分布，用于对具有重右尾的数据进行建模。采用最大似然估计法来估计模型参数。对最大似然估计量进行了简要的蒙特卡罗模拟研究。此外，还计算了一些精算度量，如风险价值和尾部风险价值。还基于这些精算度量进行了模拟研究。将 Z-Weibull 模型应用于地震保险数据。基于分析，我们观察到所提出的分布可以在保险科学和其他相关领域中对重尾数据进行建模非常有效。最后，还对地震数据进行了贝叶斯分析和 Gibbs 抽样性能分析。
