Type I heavy-tailed family of generalized Burr III distributions : properties, actuarial measures, regression and applications

This study introduces a new family of distributions (FoD) called type I heavy-tailed odd Burr III-G (TI-HT-OBIII-G) distribution. Several statistical properties of the family are derived along with actuarial risk measures. The maximum likelihood estimation (MLE) approach is adopted in the parameter estimation process. The estimates are evaluated centered on mean square errors and average bias via the Monte Carlo simulation framework. A regression model is formulated and the residual analysis is investigated. Members of the new FoD are applied to heavy-tailed data sets and compared to some well-known competing heavytailed distributions. The practicality, flexibility and importance of the new distribution in modeling is empirically proven using three data sets.