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

• Published in: Journal of statistical theory and applications Vol. 12; no. 3; pp. 225 - 244
• Main Authors: Ramos, Manoel Wallace A., Cordeiro, Gauss M., Marinho, Pedro Rafael D., Dias, Cícero Rafael B., Hamedani, G. G.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-09-2013; Springer Nature B.V; Springer
• Subjects: Economic analysis; Estimation; Generating function; Log-logistic distribution; Mean deviation; Moment; Zografos- Balakrishnan log-logistic distribution; Failure rates; Research Article; Weibull distribution; Mean deviation; Generating function; Moment; Estimation; 62E99; Zografos-Balakrishnan log-logistic distribution; Log-logistic distribution; 60E05
• ISSN: 1538-7887; 2214-1766; 1538-7887
• DOI: 10.2991/jsta.2013.12.3.2

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.