A New Five-Parameter Burr System of Distributions based on Generalized Pearson Differential Equation

This paper derives a new five-parameter family of Burr type distributions based on the generalized Pearson differential equation, which is more flexible and is a natural generalization of the Burr, GB2 and many other distributions found in literature. We refer to this new distribution as the generalized Burr (GB) distribution. Some characteristics of the newly proposed distribution are given and some distributional relationships are established. It is observed that the proposed distribution is skewed to the right and carries most of the properties of skewed distributions. The Renyi and Shannon entropies, and Song's measure for our newly proposed distributions have also been obtained. As a motivation, the statistical applications of the results based on health related data are included. It is hoped that the findings of the paper will be useful for the practitioners in various fields of theoretical and applied sciences.