The study of properties on generalized Beta distribution

Abstract

Statistical distributions such as Normal, Log-Normal, Gamma and Beta distributions have been studied to determine the fitting ability of the distributions in different field of studies. The objective of this research is to study the properties of the generalized Beta distribution which is a 6 parameter model from the Beta family as well as to evaluate the prediction level of the model. The advantages of the generalized Beta distribution is they can be very versatile and flexible where it will provide a good description to many different types of data, including unimodal, uniantimodal, increasing, decreasing, or bath-tub shape distribution depending on the parameter values. The distributions were fitted to rainfall data collected from Sg Lui, Selangor using Non-Linear Least-Squares Minimization package of a Python software with the maximum likelihood estimation as the parameter estimation method. Simulation was proceeded using Accept-Reject algorithm where their predictive level were evaluated using model selection criteria such as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE).