A Study of Properties on Generalized Beta and Mixture of Two Modified Log-normal Distributions

Ng, Dennis Wen Wei (2019) A Study of Properties on Generalized Beta and Mixture of Two Modified Log-normal Distributions. Master dissertation/thesis, UTAR.

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Abstract

The objective of this research is to study the statistical properties of two newly proposed distributions which are the generalized Beta distribution from the Beta family and the mixture of 2 modified Log-Normal distributions from the Skew Normal family (Chuah, 2016). Properties such as the moment generating function are derived for the two mentioned distributions. The advantages of the proposed distributions are their versatility and flexibility where they could provide a good description to various data with properties such as unimodal/uniantimodal increasing, decreasing, bath-tub shape distributions and etc. Other distributions such as Beta, Gauss Hypergeometric, Exponential and Gamma distributions are selected to compare their fitting ability with the proposed distributions. An empirical study is performed using simulated data and real rainfall volume data collected from Sungai Lui (river) with Maximum Likelihood Estimation (MLE) as the parameter estimation method. Model selection criteria such as Kolmogorov-Smirnov K-S test, Akaike’s Information Criteria (AIC) and Root Mean Square Error (RMSE) are used to identify the better fitted model in this study. The empirical results show that the proposed mixture is the better fit in its Skew Normal family while the proposed generalized Beta is the worst performed in its Beta family.

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