Generating Distribution Functions Based on Burr Differential Equation | Journal of Advances in ..

The Burr's scheme is one of the most well-known statistical distribution families. The re-examination of Burr's method was prompted by a renewed interest in creating more versatile statistical distributions. The distribution functions are used to express the solutions to the Burr differential equation. Burr [1] only considered 12 distribution functions known as the Burr system of distributions in the literature, despite the fact that there are several more. It was discovered while studying the Burr system that 9 of the Burr distributions are powers of cdf ′s, also known as exponentiated distributions. In terms of cdf′s, the remaining three are direct solutions. There have been no detailed studies using generator approach techniques to produce Burr distributions in the literature. This prompted us to use a generator approach to generalise solutions to the Burr differential equation. Beta generator method, exponentiated generator method, and beta-exponentiated generator method (combined beta and exponentiated generator methods) were proposed with this goal in mind. However, we will concentrate on the exponentiated generator technique in this paper since it produces cdf ′s. The other two generator method techniques produce order statistics pdfs and distributions.

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