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Bayesian Estimation Of Beta-Type Distribution Parameters Based On Grouped Data

Author

Listed:
  • Kazuhiko Kakamu

    (Graduate School of Business Administration, Kobe University)

  • Haruhisa Nishino

    (Faculty of Law, Politics and Economics, Chiba University)

Abstract

This study considers the estimation method of generalized beta (GB) distribution parameters based on grouped data from a Bayesian point of view. Because the GB distribution, which was proposed by McDonald and Xu (1995), includes several kinds of familiar distributions as special or limiting cases, it performs at least as well as those special or limiting distributions. Therefore, it is reasonable to estimate the parameters of the GB distribution. However, when the number of groups is small or when the number of parameters increases, it may become difficult to estimate the distribution parameters for grouped data using the existing estimation methods. This study uses a Tailored randomized block Metropolis?Hastings (TaRBMH) algorithm proposed by Chib and Ramamurthy (2010) to estimate the GB distribution parameters, and this method is applied to one simulated and two real datasets. Moreover, the Gini coefficients from the estimated parameters for the GB distribution are examined.

Suggested Citation

  • Kazuhiko Kakamu & Haruhisa Nishino, 2016. "Bayesian Estimation Of Beta-Type Distribution Parameters Based On Grouped Data," Discussion Papers 2016-08, Kobe University, Graduate School of Business Administration.
  • Handle: RePEc:kbb:dpaper:2016-08
    as

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    File URL: http://www.b.kobe-u.ac.jp/paper/2016_08.pdf
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    References listed on IDEAS

    as
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    2. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, vol. 42(6), pages 1115-1127, November.
    3. Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
    4. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    5. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
    6. Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
    7. Duangkamon Chotikapanich & D. S. Prasada Rao & Kam Ki Tang, 2007. "Estimating Income Inequality In China Using Grouped Data And The Generalized Beta Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(1), pages 127-147, March.
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    11. McDonald, James B & Mantrala, Anand, 1995. "The Distribution of Personal Income: Revisited," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 201-204, April-Jun.
    12. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
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    14. Gholamreza Hajargasht & William E. Griffiths & Joseph Brice & D.S. Prasada Rao & Duangkamon Chotikapanich, 2012. "Inference for Income Distributions Using Grouped Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 563-575, May.
    15. Slottje, Daniel J., 1984. "A measure of income inequality in the U.S. for the years 1952-1980 based on the beta distribution of the second kind," Economics Letters, Elsevier, vol. 15(3-4), pages 369-375.
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