Exponentiated Weibull-Geometric Distribution and its Applications

In this paper a new lifetime distribution, which is called the exponentiated Weibull-geometric (EWG) distribution, is introduced. This new distribution obtained by compounding the exponentiated Weibull and geometric distributions. The EWG distribution includes as special cases the generalized exponential-geometric (GEG), complementary Weibull-geometric (CWG), complementary exponential-geometric (CEG), exponentiated Rayleigh-geometric (ERG) and Rayleigh-geometric (RG) distributions. The hazard function of the EWG distribution can be decreasing, increasing, bathtub-shaped and unimodal among others. Several properties of the EWG distribution such as quantiles and moments, maximum likelihood estimation procedure via an EM-algorithm, R\'{e}nyi and Shannon entropies, moments of order statistics, residual life function and probability weighted moments are studied in this paper. In the end, we give two applications with real data sets to show the flexibility of the new distribution.