Abstract

Actuaries are often in search of new distributions suitable for modeling financial and insurance losses. In this work, we propose a new family of distributions, called a new beta power transformed family of distributions. A special sub-model of the proposed class, called a new beta power transformed Weibull, suitable for modeling heavy tailed data in the scenario of actuarial statistics and finance, is considered in detail. The proposed distribution possesses desirable properties relevant to actuarial sciences. Expressions for the actuarial quantities such as value at risk, tail value at risk, tailed variance and tailed variance premium are derived. A simulation study is conducted to evaluate the behavior of the proposed distribution in actuarial sciences. Some distributional properties with estimation of parameters using maximum likelihood method are also discussed. Finally, a practical application of the proposed model to insurance data is presented.

摘要

精算师经常寻找适合金融和保险损失建模的新分布。在这项工作中，我们提出了一个新的分布族，称为新的 beta 幂变换分布族。提出的类的特殊子模型，称为新的 beta 幂变换 Weibull，适用于在精算统计和金融场景中对重尾数据进行建模，被详细考虑。提议的分布具有与精算科学相关的理想特性。推导了精算数量的表达式，例如风险价值、尾部风险价值、尾部方差和尾部方差溢价。进行了一项模拟研究，以评估所提出的分布在精算科学中的行为。还讨论了使用最大似然法估计参数的一些分布特性。最后，提出了该模型在保险数据中的实际应用。