A new four - parameter lifetime distribution and its applications

A new four - parameter lifetime distribution and its 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 exponentiallogarithmic (GEL), complementary Weibull-logarithmic (CWL), complementary exponential-logarithmic (CEL), Rayleigh-logarithmic (RL) and Exponentiated Rayleigh-logarithmic (ERL) distributions. We study various properties of the new distribution and provide numerical examples to show the flexibility and potentiality of the model