Classical and Bayesian estimation for type-I extended-F family with an actuarial application

In this work, a new flexible class, called the type-I extended-F family, is proposed. A special sub-model of the proposed class, called type-I extended-Weibull (TIEx-W) distribution, is explored in detail. Basic properties of the TIEx-W distribution are provided. The parameters of the TIEx-W distribution are obtained by eight classical methods of estimation. The performance of these estimators is explored using Monte Carlo simulation results for small and large samples. Besides, the Bayesian estimation of the model parameters under different loss functions for the real data set is also provided. The importance and flexibility of the TIEx-W model are illustrated by analyzing an insurance data. The real-life insurance data illustrates that the TIEx-W distribution provides better fit as compared to competing models such as Lindley-Weibull, exponentiated Weibull, Kumaraswamy-Weibull, alpha logarithmic transformed Weibull, and beta Weibull distributions, among others.

Automated summary

A new flexible class, called the type-I extended-F family, is proposed in this study. A detailed exploration is conducted on a special sub-model of the proposed class, known as the type-I extended-Weibull (TIEx-W) distribution. The basic properties of the TIEx-W distribution are provided, and its parameters are estimated using eight classical methods. The performance of these estimators is evaluated through Monte Carlo simulation, and Bayesian estimation of the model parameters is also performed for real data. The TIEx-W distribution is shown to provide a better fit for insurance data compared to other competing models.