AMOUD-G FAMILY OF LIFETIME DISTRIBUTIONS: PROPERTIES, HAZARD-BASED REGRESSION MODELS AND APPLICATIONS TO SURVIVAL DATA

Abstract

In this article, we introduce a new family of lifetime distributions with one extra shape parameter, called the Amoud-G family, based on the cumulative hazard rate function, the well-known concept in survival and reliability analysis. Some funda- mental theoretical properties of the new family including cumulative hazard func- tion, hazard rate, retro hazard, distribution function, quantile function, residual life function, moments, entropy, among others are derived. A special case of this new family is introduced by considering Weibull distribution as the baseline distribution called Amoud-Weibull distribution. The model parameters of the Amoud-Weibull distribution are estimated using the maximum likelihood estimation technique. The proposed distribution is used to introduce a new accelerated failure time model, which has been used to produce estimations of its model parameters. The perfor- mance of the estimation approach based on the Amoud-Weibull distribution and its hazard-based regression modeling has been examined using Monte Carlo sim- ulation analysis. In addition, four examples of real-life data sets with complete and right-censored observations are examined to show the utility and superiority of the newly proposed distribution over other fundamental distributions and their hazard-based regression models in terms of the baseline Weibull distribution and its accelerated failure time model. Finally, the empirical results show that the proposed family of survival distributions provides more realistic fits than other well-known families in terms of complete and right-censored observations..