Exponentiated Weibull–Poisson distribution: Model, properties and applications

In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull–Poisson (EWP) distribution. The new distribution arises on a latent complementary risk problem base and is obtained by compounding exponentiated Weibull (EW) and Poisson distributions. This distribution contains several lifetime sub-models such as: generalized exponential-Poisson (GEP), complementary Weibull–Poisson (CWP), complementary exponential-Poisson (CEP), exponentiated Rayleigh–Poisson (ERP) and Rayleigh–Poisson (RP) distributions.We obtain several properties of the new distribution such as its probability density function, its reliability and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via an EM-algorithm is presented in this paper. Sub-models of the EWP distribution are studied in details. In the end, applications to two real data sets are given to show the flexibility and potentiality of the new distribution.