Modelling insurance losses using a new beta power transformed family of distributions

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.

Keywords:

• Actuarial measures
• estimation
• family of distributions
• financial risk
• fit
• Monte Carlo simulation
• Weibull distribution

Acknowledgment

The authors are grateful to the Editor-in-Chief, the Associate Editor and the anonymous referees for many of their valuable comments and suggestions which lead to this improved version of the paper. The first two authors also acknowledge the support of the Yazd University, Iran.

Data availability statement

This work is mainly a methodological development and has been applied on secondary data related to financial and insurance sciences, but if required, data will be provided.

Dedication

This article is drafted from the PhD work of the first author (Zubair Ahmad). The author would like to dedicate this achievement to the memory of his late parents.