The Kumaraswamy-Log-Logistic Distribution

Abstract

The log-logistic distribution is widely used in survival analysis when the failure rate function presents a unimodal shape. Based on the log-logistic and Kumaraswamy distributions, we introduce the called Kumaraswamy-log-logistic distribution. The new distribution contains several important distributions discussed in the literature as sub-models such as the log-logistic, exponentiated log-logistic and Burr XII distributions, among several others. The beauty and importance of the new distribution lies in its ability to model non-monotonic failure rate functions, which are quite common in lifetime data analysis and reliability. Some of its structural properties are studied. We propose the Kumaraswamy-logistic regression model which has, as sub-models, various widely-known regression models. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. Two real data sets illustrate the importance and flexibility of the proposed models.