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Dagum and Singh-Maddala distributions have been widely assumed as models for income distribution in empirical analyses. The properties of these distributions are well known and several estimation methods for these distributions from grouped data have been discussed widely. Moreover, previous studies argue that the Dagum distribution gives a better fit than the Singh-Maddala distribution in the empirical analyses. This study explores the reason why Dagum distribution is preferred to the Singh-Maddala distribution in terms of the Akaike Information Criterion through Monte Carlo experiments. In addition, the properties of the Gini coefficients and the top income shares from these distributions are examined by means of root mean square errors. From the experiments, we confirm that the fit of the distributions depends on the relationships and magnitudes of the parameters. Furthermore, we confirm that the root mean square errors of the Gini coefficients and top income shares depend on the relationships of the parameters when the data-generating processes are a generalized beta distribution of the second kind.

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This study considers the estimation method of generalized beta (GB) distribution parameters based on grouped data from a Bayesian point of view. Because the GB distribution, which was proposed by McDonald and Xu (1995), includes several kinds of familiar distributions as special or limiting cases, it performs at least as well as those special or limiting distributions. Therefore, it is reasonable to estimate the parameters of the GB distribution. However, when the number of groups is small or when the number of parameters increases, it may become difficult to estimate the distribution parameters for grouped data using the existing estimation methods. This study uses a Tailored randomized block Metropolis-Hastings (TaRBMH) algorithm proposed by Chib and Ramamurthy (2010) to estimate the GB distribution parameters, and this method is applied to one simulated and two real datasets. Moreover, the Gini coefficients from the estimated parameters for the GB distribution are examined.