The gamma extended Weibull family of distributions

Abstract

We introduce a new family of distributions called the gamma extended Weibull family. The proposed family includes several well-known models as special cases and defines at least seventeen new special models. Structural properties of this family are studied. Additionally, the maximum likelihood method for estimating the model parameters is discussed. An application to real data illustrates the usefulness of the new family. The results provide evidence that the proposed family outperforms other classes of lifetime models.

Keywords

• Extended Weibull distributions; Hazard rate function; Maximum likelihood estimation; Moments; Stacy’s generalized gamma distribution