The Zografos-Balakrishnan Type-I Heavy-Tailed-G Family of Distributions with Applications

Abstract

We propose a new family of distributions called the Zografos-Balakrishnan type-I heavy-tailed-G (ZBTIHT-G) distributions. A special model of the proposed family, namely Zografos-Balakrishnan type-I heavy-tailed-Weibull (ZBTIHT-W) model is thoroughly studied. Statistical properties of the new family of distributions including, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy are presented. 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 estimators of the model parameters.The flexibility and importance of the new family of distributions are demonstrated by means of applications to real data sets.