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.
Tahir, M. H.; Mansoor, Muhammad; Zubair, Muhammad; and Hamedani, Gholamhossein, "McDonald Log-Logistic Distribution with an Application to Breast Cancer Data" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 239.
Published version. Journal of Statistical Theory and Applications, Vol. 13, No. 1 (March 2014): 65-82. DOI. © 2014 The Authors. Used with permission.