Hamid Karamikabir

Statistical distributions are widely used in describing and predicting real-world phenomena. Consequently, it is very important to choose the most appropriate statistics for data modeling. In this thesis, a new class of lifetime distributions called Weibull Top-Leon distribution families is proposed. The proposed family is built through a combination of Weibull and Top Leon. General properties from the Weibull Top-Leon family, including details of density and hazard problems of limiting behavior, mixed representation, skewness and elongation, moment, moment generating function, incomplete moment generation. Various methods have been investigated for usability and numerically calculated performance scores. New family inference based on likelihood ratio statistics for testing some types of lifespan is discussed. The performance of maximum correct representation raters in terms of bias and mean squared error is simulated using a study. The concept and adoption of the new family are demonstrated using two applications for real data sets.