  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.
