A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets

The Burr Type XII distribution is commonly used in reliability analysis, survival analysis, and actuarial science to model the time-to-failure of a system or component. It is also used in finance to model the distribution of portfolio retums and in hydrology to model the frequency of extreme events. In this work, a new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based constraction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations.