Generalized beta distribution and its properties

In this study, two important types of continuous distribution functions, the beta and the generalized beta distributions, were studied and the developments of their major characterictics properties were aimed to be improved.A comprehensive knowledge of literature about distributions which are the fundamentals of mathematical statistics are given as an introductory to this research. By dealing with the previous studies, it was emphasized why beta distribution is so important in the sense of both mathematical and statistical analysis. And later, some important descriptions and consequences of the mathematical statistics were defined in subsequent sections.Part of main evidence contains Generalized Beta distribution functions and its primary features were given within the findings title. The special conditions of the generalized beta and the exponential distributions functions were examined and rebuilded. Additionally, probability charts were obtained for some constant values of the generalized beta distributions parameters. The values of parameters were assumed to have a smooth distribution and a mixture distribution was thus improved by means of this approach.Part of result and discussion contain evidences with mathematical statistic and statistical analyzes with knowledge of literature are evaluated.Key words: Beta Distribution, Generalized Beta Distribution, Gauss Hypergeometric Function, Probability tables, Mixture Distributions.