PowerBurr regression model for heavy-tailed loss data and its application

Statistical modeling of heavy-tailed loss data is a crucial foundation for catastrophe risk management. The PowerBurr distribution, as a novel multi-parameter heavy-tailed distribution, has promising applications in catastrophe risk management. This paper explores the statistical properties of the PowerBurr distribution in depth, including its special distributional forms under specific parameter settings and the limiting distributions at the boundaries of the parameter space. We further extend the concept to a family of PowerBurr distributions and analyze the tail properties of various distributions within this family. Building upon this foundation, the present study constructs a general linear regression model by specifying functional relationships between the reparameterized scale and shape parameters of the PowerBurr distribution and a set of explanatory variables. Methods for parameter estimation and model validation are provided. The commonly used Lomax regression model is a special case of this regression model. Finally, the PowerBurr-based regression model is applied to earthquake loss data in China and compared with regression models based on other heavy-tailed distributions. The results demonstrate that the new model improves the model’s goodness-of-fit and predictive performance, providing a new and effective tool for modeling heavy-tailed loss data.