The exponentiated G geometric family of distributions

Abstract

We propose a new class of distributions called the exponentiated G geometric family motivated mainly by lifetime issues which can generate several lifetime models discussed in the literature. Some mathematical properties of the new family including asymptotes and shapes, moments, quantile and generating functions, extreme values and order statistics are fully investigated. We propose the log-exponentiated Weibull geometric and log-exponentiated log-logistic geometric regression models to cope with censored data. The model parameters are estimated by maximum likelihood. Three examples with real data expose quite well the new family.

Keywords:

• censored data
• exponentiated G distribution
• generating function
• geometric distribution
• lifetime distribution
• maximum-likelihood estimation
• moment
• quantile function