A novel M-Lognormal–Burr regression model with varying threshold for modeling heavy-tailed claim severity data

Abstract

In this study, we explore the potential of composite probability distributions in effectively modeling claim severity data, which encompasses a spectrum of losses, ranging from minor to substantial. Our approach incorporates the innovative Mode-Matching technique to introduce a novel composite Lognormal–Burr distribution family. To comprehensively address the diverse risk characteristics exhibited by policyholders, we develop a regression model based on the composite Lognormal–Burr distribution. Additionally, we delve into the details of the parameter estimation method required for precise model parameter estimation. The practical utility of our proposed composite regression model is substantiated through its application to real-world insurance data, serving as a compelling illustration of its effectiveness.

Keywords:

• Burr distribution
• composite regression model
• generalized log-Moyal distribution
• heterogeneity
• mode-matching technique
• varying threshold

Acknowledgments

We thank both the referees and the Associate Editor for the constructive comments, particularly the implementation of the IPO methodology for tail index estimation. These suggestions improve the manuscript significantly.

Data Availability Statement

The data that support the findings of this study are available third party. Restrictions apply to the availability of these data, which were used under license for this study. Data are available from the authors with the permission of third party.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The present work is part of a project granted Department of Science & Technology, Government of India under the Core Research Grant scheme (CRG/2019/002993). D.B. and G.A. thank the funding agency for financial support.