The generalized odd log-logistic family of distributions: properties, regression models and applications. Issue 5 (24th March 2017)

• Record Type: Journal Article
• Authors: Cordeiro, Gauss Moutinho; Alizadeh, Morad; Ozel, Gamze; Hosseini, Bistoon; Ortega, Edwin Moises Marcos; Altun, Emrah
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 5(2017)
• Page Start: 908
• Page End: 932
• Publication Date: 2017-03-24
• Subjects: Generated family -- maximum likelihood -- moment -- odd log-logistic -- order statistic -- quantile function -- Rényi entropy; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1238088
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.