Uniform Random Sample and Symmetric Beta Distribution

N.L. Johnson and S. Kotz introduced in 1990 an interesting family of symmetric distributions which is based on randomly weighted average from uniform random samples. The only example that could be addressed to their work is the so-called "uniformly randomly modified tin" distribution from which two random samples have been computed. In this paper, we generalize a subfamily of their symmetric distributions and identify a concrete instance of this generalized subfamily. That instance turns out to belong to the family of Johnson and Kotz, which had not seemingly received proper attention in the literature

Estimating Income Inequality in China Using Grouped Data and the Generalized Beta Distribution

Gini coefficient, generalized beta distribution, urban and rural inequality

GMM Estimation of Income Distributions from Grouped Data

We develop a GMM procedure for estimating income distributions from grouped data with unknown group bounds. The approach enables us to obtain standard errors for the estimated parameters and functions of the parameters, such as inequality and poverty measures, and to test the validity of an assumed distribution using a J-test. Using eight countries/regions for the year 2005, we show how the methodology can be applied to estimate the parameters of the generalized beta distribution of the second kind, and its special-case distributions, the beta-2, Singh-Maddala, Dagum, generalized gamma and lognormal distributions. This work extends earlier work (Chotikapanich et al., 2007, 2012) that did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and considered only the beta-2 distribution. The results show that generalized beta distribution fits the data well and outperforms other frequently used distributions.GMM; generalized beta distribution; grouped data; inequality and poverty