Morad Alizadeh

In this thesis, a new class of continuous distributions is introduced under the name of Top­Leon odd log logistic fortune family and weighted Top­Leon family. Some of the mathematical properties of these families, such as the Hazard rate, asymptotes, quantile function, normal and conditional moments, average deviations, ordinal statistics, etc ,are investigated. Also, a special case for each family is introduced under the title of Top­Leon odd log logistic Lindley distribution and weighted Top­Leon lindley and some of its properties are also examined. Also, maximum likelihood estimation and inference on model parameters are discussed. By simulating the behavior of maximum likelihood estimation, it is studied. Finally, by presenting two real data sets, we examine the superiority of the model’s fit compared to other models.