Generating Distribution Functions Based on Burr Differential Equation

Abstract

One of the most prominent families of statistical distributions is the Burr’s system. Recent renewed interest in developing more flexible statistical distributions led to the re-examination of Burr’s system. Solutions of Burr differential equation are expressed in terms of distribution functions. Burr [1] considered only 12 distribution functions known in literature as the Burr system of distributions, yet there are more than that in number. Studying the Burr system, it was realized that 9 of the Burr distributions are powers of cdf ′s, popularly now known as exponentiated distributions. The remaining 3 are direct solutions in terms of cdf′s. Detailed studies using generator approach techniques to generate Burr distributions has not been undertaken in literature. This motivated us to generalize solutions of Burr differential equation by generator approach. With this aim in mind, beta generator method, exponentiated generator method and beta-exponentiated generator method (a combination of beta and exponentiated generator methods) was proposed. However in this paper, we will focus on exponentiated generator technique as it generates cdf ′s. The other two generator approach techniques generate pdf′s and distributions of order statistics.