The Zografos-Balakrishnan Log-Logistic Distribution: Properties and Applications

The log-logistic distribution (also known as the Fisk distribution in economics) is widely used in survival analysis when the failure rate function presents a unimodal shape.In this paper, we introduce the Zografos-Balakrishnan log-logistic distribution, which contains the log-logistic distribution as a special model and has the four common shapes of the hazard hate function.We present some properties of the new distribution and estimate the model parameters by maximum likelihood.An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models such as the exponentiated Weibull distribution.