Two New Classes of Generalized Modified Weibull Distributions with Application to Lifetime Data

Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail two new classes of distributions, namely, Gamma-Weibull-G family of distributions (GWG) and gamma-exponentiated or generalized modified Weibull (GEMW) distribution. Some special models in these new classes are discussed. Statistical properties of these 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. For the GEMW, we also present Renyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data