A new heavy-tailed exponentiated generalised-G family of distributions: properties and applications

In this paper, we introduce a new family of heavy-tailed distributions called the type-I heavy-tailed exponentiated generalised-G (TIHTEG-G) family of distributions. A special model of the proposed family, namely the type-I heavy-tailed exponentiated generalised-log-logistic (TIHTEG-LLoG) model is studied in detail. Statistical properties of the new family of distributions are presented. These include, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy. The maximum likelihood method of estimation is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the model. Actuarial measures are also derived and simulation study for these measures is done to show that the proposed TIHTEG-LLoG model is a heavy-tailed model. Real datasets are analysed to illustrate the usefulness of the proposed model.