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Modeling Income Distributions Using Elevated Distributions On A Bounded Domain

In: Distribution Models Theory

Author

Listed:
  • J. RENÉ VAN DORP

    (Engineering Management and Systems Engineering Department, The George Washington University, 1776 G street, Suite 110, NW, Washington DC, 20052, USA)

  • SAMUEL KOTZ

    (Engineering Management and Systems Engineering Department, The George Washington University, 1776 G street, Suite 110, NW, Washington DC, 20052, USA)

Abstract

This paper presents a new two parameter family of continuous distribution on a bounded domain which has an elevated but finite density value at its lower bound. Such a characteristic appears to be useful, for example, when representing income distributions at lower income ranges. The family generalizes the one parameter Topp and Leone distribution originated in the 1950's and recently rediscovered. The family of beta distributions has been used for modeling bounded income distribution phenomena, but it only allows for an infinite and zero density values at its lower bound, and a constant density of 1 in case of its uniform member. The proposed family alleviates this apparent jump discontinuity at the lower bound. The U.S. Income distribution data for the year 2001 is used to fit distributions for Caucasian (Non-Hispanic), Hispanic and African-American populations via a maximum likelihood procedure. The results reveal stochastic ordering when comparing the Caucasian (Non-Hispanic) income distribution to that of the Hispanic or African-American population. The latter indicates that although substantial advances have reportedly been made in reducing the income distribution gap amongst different ethnic groups in the U.S. during the last 20 years or so, these differences still exist.

Suggested Citation

  • J. René Van Dorp & Samuel Kotz, 2006. "Modeling Income Distributions Using Elevated Distributions On A Bounded Domain," World Scientific Book Chapters, in: Rafael Herrerías Pleguezuelo & José Callejón Céspedes & José Manuel Herrerías Velasco (ed.), Distribution Models Theory, chapter 1, pages 1-25, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812772992_0001
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    Citations

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    Cited by:

    1. S. Nadarajah & S. Bakar, 2013. "A new R package for actuarial survival models," Computational Statistics, Springer, vol. 28(5), pages 2139-2160, October.
    2. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    3. David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.

    More about this item

    Keywords

    Inference; Uncertainty; Copulas; Stochastic Dominance; Bayesian Techniques; Hierarchical Bayesian Model; Poisson-Gamma-Gamma Model; Experience Rating; Specific Fecundity Rates; Fecundity Curves; Topp and Leone Distributions; Waring Distribution; Factorial; Cluster; Discrimination Analyses; Survival Functions;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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