Bayesian Estimation of Beta-type Distribution Parameters Based on Grouped Data

Abstract

This study considers a method of estimating generalized beta (GB) distribution parameters based on grouped data from a Bayesian point of view and explores the possibility of the GB distribution focusing on the goodness-of-fit because the GB distribution is one of the most typical five-parameter distributions. It uses a tailored randomized block Metropolis–Hastings (TaRBMH) algorithm to estimate the GB distribution parameters and this method is then applied to one simulated and two real datasets. Moreover, the fit of the GB distribution is compared with those of the generalized beta distribution of the second kind (GB2 distribution) and Dagum (DA) distribution by using the marginal likelihood. The estimation results of simulated and real datasets show that the GB distributions are preferred to the DA distributions in general, while the GB2 distributions have similar performances to the GB distributions. In other words, the GB2 distribution could be adopted as well as the GB distribution in terms of the smallest possible number of parameters, although our TaRBMH algorithm can estimate the GB distribution parameters efficiently and accurately. The accuracy of the Gini coefficients also suggests the use of the GB2 distributions.