New Four- and Five-Parameter Models for Income Distributions

  • William J. Reed
  • Fan Wu
Part of the Economic Studies in Equality, Social Exclusion and Well-Being book series (EIAP, volume 5)


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.


Income Distribution Geometric Brownian Motion Generalize Beta Luxembourg Income Study Generalize Beta Distribution 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • William J. Reed
    • 1
  • Fan Wu
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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