The exponentiated discrete Weibull distribution

In this paper, the exponentiated discrete Weibull distribution is introduced. This new generalization of the discrete Weibull distribution can also be considered as a discrete analog of the exponentiated Weibull distribution. A special case of this exponentiated discrete Weibull distribution defines a new generalization of the discrete Rayleigh distribution for the first time in the literature. In addition, discrete generalized exponential and geometric distributions are some special sub-models of the new distribution. Here, some basic distributional properties, moments, and order statistics of this new discrete distribution are studied. We will see that the hazard rate function can be increasing, decreasing, bathtub, and upside-down bathtub shaped. Estimation of the parameters is illustrated using the maximum likelihood method. The model with a real data set is also examined.