The Burr XII System of densities: properties, regression model and applications

• Published in: Journal of statistical computation and simulation Vol. 88; no. 3; pp. 432 - 456
• Main Authors: Cordeiro, Gauss M., Yousof, Haitham M., Ramires, Thiago G., Ortega, Edwin M. M.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 11-02-2018; Taylor & Francis Ltd
• Subjects: Burr XII distribution; Computer simulation; Economic models; generating function; maximum likelihood estimation; Maximum likelihood estimators; moment; Parameter estimation; quantile function; Regression analysis; regression model; Regression models
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2017.1392524

We introduce a new class of distributions called the Burr XII system of densities with two extra positive parameters. We provide a comprehensive treatment of some of its mathematical properties. We estimate the model parameters by maximum likelihood. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. We also introduce a new family of regression models based on this system of densities. The usefulness of the proposed models is illustrated by means of three real data sets.