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A generalization of generalized beta distributions

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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.

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  • 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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    1. Arthur B. Kennickell & Martha Starr-McCluer & Annika E. Sunden, 1997. "Family Finance 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.), vol. 83(1), pages .1-24, January.
    2. 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.
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    5. 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.
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    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. 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.
    4. Dmitry I. Malakhov & Nikolay P. Pilnik & Igor G. Pospelov, 2015. "Stability of Distribution of Relative Sizes of Banks as an Argument for the Use of the Representative Agent Concept," HSE Working papers WP BRP 116/EC/2015, National Research University Higher School of Economics.
    5. 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.
    6. Tevfik Aktekin & Nicholas G. Polson & Refik Soyer, 2020. "A family of multivariate non‐gaussian time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 691-721, September.

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