The Odd Log-Logistic Burr-X Family of Distributions: Properties and Applications

Abstract

In this paper, a new class of distributions called the odd log-logistic Burr-X family with two extra positive parameters is introduced and studied. The new generator extends the odd log-logistic and Burr X distributions among several other well-known distributions. We provide some mathematical properties of the new family including asymptotics, moments, moment-generating function and incomplete moments. Different methods have been used to estimate its parameters such as maximum likelihood, least squares, weighted least squares, Cramer–von-Mises, Anderson–Darling and right-tailed Anderson–Darling methods. We evaluate the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. Finally, the usefulness of the family is illustrated by means of three real data sets. The new models provide consistently better fits than other competitive models for these data sets. The new family is suitable for fitting different real data sets, the odd log-logistic Burr-X Normal model is used for modeling bimodal and skewed data sets and can be sued as an alternative to the gamma-normal, beta-normal, McDonald-normal, Marshall-Olkin-normal, Kumaraswamy-normal, Zografos-Balakrishnan and Log-normal distributions.

Keywords

• Odd log-logistic-G family
• Burr-X family
• Maximum likelihood method
• Least square method
• Weighted least square method
• Moments