McDonald log-logistic distribution with an application to breast cancer data
Muhammad Hussain Tahir, Muhammad Hadi Mansoor, Muhammad Zubair, Gholamhossein G. Hamedani · Journal of Statistical Theory and Applications · 2014
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.