Mathematics is the science of order, and its subject is to find, describe and understand the order that lies in apparently complex situations, and the basic tools of this science are the concepts that enable us to describe this order. This article has been written under the title of mathematical features and characteristics of BURR XII-BURR XIl distribution, and in fact, the purpose of this research is to investigate the mathematical characteristics and characteristics of BURR XII-BURR XIl distribution. In this research, maximum likelihood method is used to estimate unknown parameters and a new continuous distribution named Burr XII-Burr XII distribution is introduced. Some of its properties are derived. A detailed schedule is provided to demonstrate the new significance. The new model is proportional to the other models; Models associated with the lowest values for A-IC, B-IC, CA-IC and HQ-IC. Based on the above, he analyzed the research and after analyzing and reviewing the research results, he showed that the characteristics are presented based on two short moments, risk performance and also based on conditional expectation.