基于韦布尔分布的回火Pareto模型
Tempered Pareto-type modelling using Weibull distributions
摘要：
在重尾模型的各种应用中，假设的帕累托行为最终在最大数据的范围内得到缓和。在保险应用中，索赔支付受到索赔管理的影响，并且索赔可能例如在最高损害水平下经受更高水平的检查，从而导致比模态索赔明显更弱的尾部。推广Meerschaert et al.（2012）和Raschke（2019）的早期结果，在本文中，我们考虑了Pareto型分布与一般韦布尔分布在峰值阈值方法中的回火。这需要根据所选择的阈值来调制回火参数。为了避免在高分位数时高估风险价值（VaR）等风险度量，对这种调节效应进行建模非常重要。我们使用伪极大似然方法来估计模型参数，并考虑极端分位数的估计。我们得到基本的渐近结果的估计，仿真实验和应用开发的技术，火灾和责任保险数据，提供深入了解的相关性的回火组件在重尾建模的插图。
英文摘要：
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance be subject to a higher level of inspection at highest damage levels leading to weaker tails than apparent from modal claims. Generalizing earlier results of Meerschaert et al. (2012) and Raschke (2019), in this paper we consider tempering of a Pareto-type distribution with a general Weibull distribution in a peaks-over-threshold approach. This requires to modulate the tempering parameters as a function of the chosen threshold. Modelling such a tempering effect is important in order to avoid overestimation of risk measures such as the Value-at-Risk (VaR) at high quantiles. We use a pseudo maximum likelihood approach to estimate the model parameters, and consider the estimation of extreme quantiles. We derive basic asymptotic results for the estimators, give illustrations with simulation experiments and apply the developed techniques to fire and liability insurance data, providing insight into the relevance of the tempering component in heavy-tail modelling.
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