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.Electronic supplementary materialThe online version of this article (doi:10.1186/s40064-016-2007-x) contains supplementary material, which is available to authorized users.

On the Log-Logistic Distribution and Its Generalizations: A Survey

“…In terms of applications, the log-logistic distribution and its generalizations have become the most popular models for survival and reliability data. Some recent applications have included: modeling for AIDS and Melanoma data (de Santana, Ortega, Cordeiro, & Silva, 2012); used for minification process (Gui, 2013); modeling breast cancer data (Ramos et al 2013); (Tahir et al 2014); modeling on censored survival data (Lemonte, 2014); modeling time up to first calving of cows (Louzada & Granzotto, 2016); modeling, inference, and use to a polled Tabapua Race Time up to First Calving Data (Granzotto et al 2017); modeling positive real data in many areas (Lima & Cordeiro, 2017); analysing a right-censored data (Shakhatreh, 2018); modeling lung cancer data (Alshangiti, et al 2016); and modeling of breaking stress data (Aldahlan, 2020).…”

“…Other authors who studied the further results involving reliability analysis, the estimation of the parameters and the uses of the Marshall-Olkin log-logistic distribution are (Alshangiti et al 2016), and (Shakhatreh, 2018), (Nasiru et al 2019) 4.1.5 The Alpha Power Transformation Mahdavi and Kundu (2017) proposed a new generator technique that many authors applied to introduce for new statistical distributions to increase flexibility of the given family. The technique adds a new parameter to the baseline distribution.…”