Abstract
Two parametric models for income distributions are introduced. The models fitted to log(income) are the 4-parameter normal-Laplace (NL) and the 5-parameter generalized normal-Laplace (GNL) distributions. The NL model for log(income) is equivalent to the double-Pareto lognormal (dPlN) distribution applied to income itself. Definitions and properties are presented along with methods for maximum likelihood estimation of parameters. Both models along with 4- and 5-parameter beta distributions, are fitted to nine empirical distributions of family income. In all cases the 4-parameter NL distribution fits better than the 5-parameter generalized beta distribution. The 5-parameter GNL distribution provides an even better fit. However fitting of the GNL is numerically slow, since there are no closed-form expressions for its density or cumulative distribution functions. Given that a fairly recent study involving 83 empirical income distributions (including the nine used in this paper) found the 5-parameter beta distribution to be the best fitting, the results would suggest that the NL be seriously considered as a parametric model for income distributions.
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Reed, W.J., Wu, F. (2008). New Four- and Five-Parameter Models for Income Distributions. In: Chotikapanich, D. (eds) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72796-7_11
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DOI: https://doi.org/10.1007/978-0-387-72796-7_11
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