The generalized modified Weibull power series distribution: Theory and applications

A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formula for the elements of the Fisher information matrix. We consider the EM-algorithm for computing the estimates. Simulation studies and two real data set applications are also given for illustration of the flexibility and potentiality of the new distribution.