Generalized extended Weibull power series family of distributions

Abstract

In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions.The compounding procedure follows the same setup carried out by Adamidis (1998).The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions.Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. ( 2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012).Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function.The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class.An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates.Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.