Advertisement

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)

Abstract

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.

Keywords

Failure Rate Income Distribution Hazard Rate Weibull Distribution Pareto Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitchison, J. and J. A. C. Brown (1957) The Lognormal Distribution with Special Reference to its Uses in Enonomics, Cambridge University Press, Cambridge. Google Scholar
  2. Atkinson, A. B. (1970) On the Measurement of Inequality, Journal of Economic Theory, 2, 244-263.CrossRefGoogle Scholar
  3. Barlow, R. E. and F. Proschan (1965) Mathematical Theory of Reliability, Wiley, New York.Google Scholar
  4. Burr, I. W. (1942) Cumulative Frequency Functions, Annals of Mathematical Statistics, 13, 215-235.CrossRefGoogle Scholar
  5. Champernowne, D. G. (1953) A Model of Income Distribution, Economic Journal, 63(2), 318-351.CrossRefGoogle Scholar
  6. Cramer, J. S. (1971) Empirical Econometrics, North Holland, Amsterdam.Google Scholar
  7. Fisk, P. R. (1961) The Graduation of Income Distributions, Econometrica, 29(2), 171-185.CrossRefGoogle Scholar
  8. Gastwirth, J. L. (1972) The Estimation of the Lorenz Curve and Gini Index, Review of Economics and Statistics, 54, 306-316.CrossRefGoogle Scholar
  9. Gastwirth, J. L. and J. T. Smith (1972) A New Goodness-of-Fit-Test, ASA Proceedings of the Business and Economic Statistics Section, pp. 320-322.Google Scholar
  10. Jorgenson, D. J., J. J. McCall and R. Radner (1967) Optimal Replacement Policy, North Holland, Amsterdam. Google Scholar
  11. Lotka, A. J. (1956) Elements of Mathematical Biology, Dover, New York.Google Scholar
  12. Mandelbrot, B. (1960) The Pareto-L évy Law and the Distribution of Income, International Economic Review, 1, 79-106.CrossRefGoogle Scholar
  13. Rutherford, R. S. G. (1955) Income Distributions: A New Model, Econometrica, 23(3), 277-294.CrossRefGoogle Scholar
  14. Salem, A. B. Z. and T. D. Mount (1974) A Convenient Descriptive Model of Income Distribution: the Gamma Density, Econometrica, 42(6), 1115-1127.CrossRefGoogle Scholar
  15. US Bureau of the Census (1960-1972) Current Population Reports, Series P-60 and P-20, US Government Printing Office, Washington.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • S. K. Singh
  • G. S. Maddala

There are no affiliations available

Personalised recommendations