Modelling insurance losses using a new beta power transformed family of distributions
Zubair Ahmad, Eisa Mahmoudi, Morad Alizadeh
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.