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.