The Kumaraswamy-Generalized Gamma Distribution with Application in Survival Analysis

Based on the Kumaraswamy distribution (Jones, 2009), we study the so-called Kum-generalized gamma distribution that is capable of modeling bathtub-shaped hazard rate functions. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models such as the exponentiated generalized gamma, exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma, generalized Rayleigh, among several others. Some mathematical properties of the Kum-generalized gamma distribution are studied. We obtain two infinite sum representations for the moments and for the moment generating function. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. Two real data sets are analyzed with this distribution.