The Gamma-Weibull-G Family of Distributions with Applications

Abstract

Weibull distribution and its extended families has been widely studied in lifetime ap- plications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-Weibull- G (GWG) family of distributions. Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. We also present R´enyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data sets.