GENERALIZATION OF BURR DISTRIBUTION AND INTRODUCTION OF A NEW FAMILY OF STATISTICAL DISTRIBUTIONS

The family of Burr distributions consists of twelve different distributions that result from solving a differential equation. This family is part of the family of continuous distributions and its applications have been investigated in various topics such as survival function, simulation problems, and economic and insurance analyses. Since the flexibility of the generalized distributions is often greater than the distribution itself, the generalization of the distributions of this family is of great interest. Also, due to the diversity of the distribution type, various generalizations of the Burr distribution have been presented. Regarding the importance of generalized distributions in this family, it is enough that the family of Burr distributions can be considered a parametric generalized family. In this article, it is intended to present a generalization of the Burr distribution, which results in the special case of the type II Burr distribution; In this way, we add a parameter in the type II Burr distribution structure and by changing this parameter, we reach different Burr distributions, including the type II Burr distribution. The mentioned parameter along with other distribution parameters is estimated by the maximum likelihood method.