Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation

This paper compares the goodness-of-fit of two new types of parametric income distribution models (PIDMs), the kappa-generalized (kG) and double-Pareto lognormal (dPLN) distributions, with that of beta-type PIDMs using US and Italian data for the 2000s. A three-parameter model kG tends to estimate the Lorenz curve and income inequality indices more accurately when the likelihood value is similar to that of the beta-type PIDMs. For the first half of the 2000s in the USA, the kG outperforms the other PIDMs in goodness-of-fit evaluated by both frequency-based criteria (such as the maximum likelihood value) and money-amount-based criteria (such as accuracy of estimation of the Lorenz curve). A four-parameter model dPLN generally outperforms the GB2 in both criteria. Furthermore, when the overall income distribution is approximated by a mixture of distributions fitted separately for each age class of the household heads (the ‘MLE-by-Age' method), the goodness-of-fit of the dPLN mixture model is found to be comparable to or higher than that of all of the PIDMs in the ordinary MLE fit, and, in the overall evaluation, this mixture model outperforms all of the single PIDMs in the sense that it is better fitted according to at least in one of the two criteria in almost all cases. The dPLN and its mixture model are found to have an explicit analytic expression for the Gini coefficient. The dPLN is therefore also suitable for the MLE-by-Age method in this respect.