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A generalization of generalized beta distributions

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  • Michael B. Gordy

Abstract

This paper introduces the ``compound confluent hypergeometric'' (CCH) distribution. The CCH unifies and generalizes three recently introduced generalizations of the beta distribution: the Gauss hypergeometric (GH) distribution of Armero and Bayarri (1994), the generalized beta (GB) distribution of McDonald and Xu (1995), and the confluent hypergeometric (CH) distribution of Gordy (forthcoming). Unlike the beta, GB and GH, the CCH allows for conditioning on explanatory variables in a natural and convenient way. The CCH family is conjugate for gamma distributed signals, and so may also prove useful in Bayesian analysis. Application of the CCH is demonstrated with two measures of household liquid assets. In each case, the CCH yields a statistically significant improvement in fit over the more restrictive alternatives.

Suggested Citation

  • Michael B. Gordy, 1998. "A generalization of generalized beta distributions," Finance and Economics Discussion Series 1998-18, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:1998-18
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    References listed on IDEAS

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    1. Christopher D. Carroll, 1992. "The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 23(2), pages 61-156.
    2. Arthur B. Kennickell & Martha Starr-McCluer & Annika E. Sunden, 1997. "Family finances in the U.S.: recent evidence from the Survey of Consumer Finances," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Jan, pages 1-24.
    3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    4. James M. Poterba & Andrew Samwick, 2001. "Household Portfolio Allocation over the Life Cycle," NBER Chapters,in: Aging Issues in the United States and Japan, pages 65-104 National Bureau of Economic Research, Inc.
    5. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
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    Cited by:

    1. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2008. "Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 149-184, June.
    2. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2003. "Poverty, Income Distribution and CGE Modeling: Does the Functional Form of Distribution Matter?," Cahiers de recherche 0332, CIRPEE.
    3. D. Boccanfuso & F. Cabral & F. Cissé & A. Diagne & L. Savard, 2003. "Pauvreté et distribution de revenus au Sénégal: une approche par la modélisation en équilibre général calculable micro-simulé," Cahiers de recherche 0333, CIRPEE.

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    Keywords

    Econometric models ; Statistics;

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