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Bayesian estimation of the Bonferroni index from a Pareto-type I population

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  • G. M. Giorgi

    (Università “La Sapienza”)

  • M. Crescenzi

    (Università “La Sapienza”)

Abstract

Summary The Bonferroni index (B) is a measure of income and wealth inequality, and it is particularly suitable for poverty studies. Since most income surveys are of a sample nature, we propose Bayes estimators ofB from a Pareto/I population. The Bayesian estimators are obtained assuming a squared error loss function and, as prior distributions, the truncated Erlang density and the translated exponential one. Two different procedures are developed for a censored sample and for income data grouped in classes.

Suggested Citation

  • G. M. Giorgi & M. Crescenzi, 2001. "Bayesian estimation of the Bonferroni index from a Pareto-type I population," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 41-48, January.
    • Handle: RePEc:spr:stmapp:v:10:y:2001:i:1:d:10.1007_bf02511638
    DOI: 10.1007/BF02511638
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    1. Giovanni Maria Giorgi & Michele Crescenzi, 2001. "A proposal of poverty measures based on the Bonferroni inequality index," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 3-16.
    2. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    3. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    4. Arnold, Barry C. & Press, S. James, 1983. "Bayesian inference for pareto populations," Journal of Econometrics, Elsevier, vol. 21(3), pages 287-306, April.
    5. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-759, May.
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    Cited by:

    1. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    2. Giovanni M. Giorgi & Alessio Guandalini, 2018. "Decomposing the Bonferroni Inequality Index by Subgroups: Shapley Value and Balance of Inequality," Econometrics, MDPI, vol. 6(2), pages 1-16, April.
    3. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    4. Walter Piesch, 2005. "Bonferroni-Index und De Vergottini-Index. Zum 75. und 65. Geburtstag zweier fast vergessener Ungleichheitsmaße," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 259/2005, Department of Economics, University of Hohenheim, Germany.
    5. Satya R. Chakravarty & Pietro Muliere, 2004. "Welfare indicators: a review and new perspectives. 2. Measurement of poverty," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 247-281.
    6. Elena Bárcena-Martin & Jacques Silber, 2017. "The Bonferroni index and the measurement of distributional change," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 1-16, April.

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    More about this item

    Keywords

    Bonferroni inequality index; Bayes estimator; Pareto/I distribution; truncated Erlang distribution; translated exponential distribution; squared error loss function;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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