A new extension of the Burr XII distribution generated by odd log-logistic random variables

Abstract

Irving W. Burr pioneered the introduction of the Burr XII model which is commonly used in reliability and medical studies. Based on this distribution, we propose a new model called the odd-log-logistic Burr XII distribution for describing lifetime data. It contains several special models such as the log-logistic, Weibull and Burr XII distributions, among several others and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of Burr XII densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, cumulants and generating function are derived. We discuss the method of maximum likelihood to fit the model parameters for censored data. For different parameter settings and sample sizes, various simulation cenarious are performed and compared in order to study the performance of the new distribution. The superiority of the proposed lifetime model is illustrated by means of two real data sets.