Exponentiated Weibull-logarithmic Distribution: Model, Properties and   Applications
  In this paper, we introduce a new four-parameter generalization of the exponentiated Weibull (EW) distribution, called the exponentiated Weibull-logarithmic (EWL) distribution, which obtained by compounding EW and logarithmic distributions. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters and contains several lifetime sub-models such as: generalized exponential-logarithmic (GEL), complementary Weibull-logarithmic (CWL), complementary exponential-logarithmic (CEL), exponentiated Rayleigh-logarithmic (ERL) and Rayleigh-logarithmic (RL) distributions. We study various properties of the new distribution and provide numerical examples to show the flexibility and potentiality of the model. 
Eisa Mahmoudi, Afsaneh Sepahdar, Artur Lemonte
stat.ME