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.