The compound class of extended Weibull power series distributions

We introduce a general method for obtaining more flexible new distributions by compounding the extended Weibull and power series distributions. The compounding procedure follows the same set-up carried out by Adamidis and Loukas (1998) and defines 68 new sub-models. The new class of generated distributions includes some well-known mixing distributions, such as the Weibull power series (Morais and Barreto-Souza, 2011) and exponential power series (Chahkandi and Ganjali, 2009) distributions. Some mathematical properties of the new class are studied including moments and the generating function. We provide the density function of the order statistics and their moments. The method of maximum likelihood is used for estimating the model parameters. Special distributions are investigated. We illustrate the usefulness of the new distributions by means of two applications to real data sets.