A Function for Size Distribution of Incomes

  • S. K. Singh
  • G. S. Maddala
Part of the Economic Studies in Equality, Social Exclusion and Well-Being book series (EIAP, volume 5)


The paper derives a function that describes the size distribution of incomes. The two functions most often used are the Pareto and the lognormal. The Pareto function fits the data fairly well towards the higher levels but the fit is poor towards the low income levels. The lognormal fits the lower income levels better but its fit towards the upper end is far from satisfactory. There have been other distributions suggested by Champernowne, Rutherford, and others, but even these do not result in any considerable improvement. The present paper derives a distribution that is a generalization of the Pareto distribution and the Weibull distribution used in analyses of equipment failures. The distribution fits actual data remarkably well compared with the Pareto and the lognormal.


Failure Rate Income Distribution Hazard Rate Weibull Distribution Pareto Distribution 
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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • S. K. Singh
  • G. S. Maddala

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