This dissertation extends the characterization of maximum Shannon entropy models to derive some maximum entropy models of discrete and continuous univariate probability distributions. The extension is made through making use of Burg, Gini index, Kapur Bayesian, Ebanks, Forte entropy and Kullback-Leibler for both discrete and continuous random variables, under the assumption of some moment constraints, such as: Arithmetic mean, geometric mean, and other moments.
In addition, this research uses the Lagrangian method and the calculus of variation theorem to derive the intended maximum entropy models. It also uses Mathematica program to solve the system of equations and to find the characterstics of the resulted maximum entropy models. Meanwhile, this research uses numerical computations or analytic techniques, if possible, to evaluate the properties of the new generated distributions.
Most of derives maximum entropy models are new, but some of them are known as: binomial, Bernolli, Pareto, and Poisson distributions. Finally, the research proves about six new theorems and obtains the characterization of maximum entropy models (about 16 new distributions).