Exponentiated Weibull-logarithmic Distribution: Model, Properties and Applications

Abstract

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.

arXiv admin note: substantial text overlap with arXiv:1212.5586, arXiv:1212.5613, arXiv:1206.4008; and text overlap with arXiv:0809.2703 by other authors