title: Further results involving Marshall-Olkin log-logistic distribution: reliability analysis, estimation of the parameter, and applications.
abstract: The purpose of this paper is to provide further study of the Marshall-Olkin log-logistic model that was first described by Gui (Appl Math Sci 7:3947-3961, 2013). This model is both useful and practical in areas such as reliability and life testing. Some statistical and reliability properties of this model are presented including moments, reversed hazard rate and mean residual life functions, among others. Maximum likelihood estimation of the parameters of the model is discussed. Finally, a real data set is analyzed and it is observed that the presented model provides a better fit than the log-logistic model.
authors.affiliation: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451 Kingdom of Saudi Arabia.
authors.forename: Arwa M
authors.initials: AM
authors.lastname: Alshangiti
authors.affiliation: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451 Kingdom of Saudi Arabia.
authors.forename: M
authors.initials: M
authors.lastname: Kayid
authors.affiliation: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451 Kingdom of Saudi Arabia.
authors.forename: B
authors.initials: B
authors.lastname: Alarfaj
keywords: Applications; Marshall–Olkin; Maximum likelihood estimates; Mean inactivity time function; Mean residual life function; Reversed hazard rate function