The odd log–logistic normal distribution: Theory and applications in analysis of experiments. (2nd April 2016)

• Record Type: Journal Article
• Authors: da Silva Braga, Altemir; Cordeiro, Gauss M.; Ortega, Edwin M. M.; Nilton da Cruz, José
• Is Part Of: Journal of statistical theory and practice. Volume 10:Number 2(2016)
• Page Start: 311
• Page End: 335
• Publication Date: 2016-04-02
• Subjects: Generating function -- log–logistic distribution -- maximum likelihood estimation -- mean deviation -- normal distribution -- regression model; 62E15 -- 62F10 -- 62F40 -- 62J05 -- 62N02 -- 62P30 -- 05B05 -- 62B15; 519.505
• DOI: 10.1080/15598608.2016.1141127
• Languages: English
• ISSNs: 1559-8608

Abstract

ABSTRACT: Providing a new distribution is always precious for statisticians. A new three–parameter model called the odd log–logistic normal (OLLN) distribution is defined and studied. The distribution is symmetric, platykurtic, leptokurtic, and may be unimodal or bimodal. Various structural properties are derived, including explicit expressions for the ordinary and incomplete moments, generating function, and mean deviations. We use maximum likelihood to estimate the parameters of the new model. We prove empirically that the proposed distribution is a very competitive model to other classical models by means of three real data sets with one example in analysis of experiments. We can conclude that this model can give more realistic fits than other special regression models.