The generalized entropy methods based on moment constraints

MaxEnt, MinxEnt entropy optimization distributions have important applications in many fields such as particularly statistics, economy, engineering, space sciences and other fields, by virtue of success in the solving of several problems. Recently, MinMaxEnt, MaxMaxEnt, MaxMinxEnt, MinMinxEnt distributions, which are important generalizations of these distributions in terms of modelling statistical data, have been defined and applied in literature. However, many difficulties are encountered to obtain entropy optimization distributions and generalized entropy optimization distributions for continuous random variables due to certain properties of these distributions.In this thesis, a numerical method based on the Gauss-Legendre approach, which is assigned to obtain MaxEnt, MinxEnt entropy optimization distributions and MinMaxEnt, MaxMaxEnt, MaxMinxEnt, MinMinxEnt generalized entropy optimization distributions for continuous random variables, is developed. We call this method as the method based on Gauss-Legendre approach. Various statistical data is modelled via generalized entropy optimization distributions obtained by means of the method based on Gauss-Legendre approach. The goodness of the distributions, which are obtained through this method is presented with statistical tests and criteria.