Format of Original
Journal of Statistical Theory and Applications
Original Item ID
We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit than other important lifetime models.