Asymptotic Distributions of Indices of Concentration: Empirical Verification and Applications

  • Giovanni Latorre
Part of the Studies in Contemporary Economics book series (CONTEMPORARY)


The increasing use of the asymptotic methodology, as a mean to derive sling distributions of indices of concentration [see Schmittlein (1983); Latorre (1987; 1988)], makes it necessary to check whether the large sle results are verified at the sle sizes currently in use in the income surveys. Taking into account that such asymptotic sling distributions are normal with known mean and variance, the above problem essentially consists in finding out the finite sle sizes from which such normality is fully verified.


Concentration Index Population Parameter Coverage Probability Simulated Distribution Lognormal Model 
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  1. Banca d Italia, (1983). L’indagine cionaria sui bilanci delle famiglie italiane: Nota Metodologica. Bollettino Statistico, n. 3–4.Google Scholar
  2. Banca d’ltalia, (1984). I bilanci delle famiglie italiane nell–anno 1983. Bollettino Statistico, n. 3–4.Google Scholar
  3. Conover, W. J., (1980). Practical nonparametric statistics, J. Wiley & Sons, New York.Google Scholar
  4. Dagum, C., (1977). A new model of personal income distribution: specification and estimation. Economie Appliquée, vol.XXX, n. 3.Google Scholar
  5. Dagum, C. - Lemmi, A., (1987). A contribution to the analysis of income distribution and income inequality, and a case study: Italy. Research Paper n. 8706, Faculty of Social Sciences, Dept. of Economics, University of Ottawa.Google Scholar
  6. Dallal, G. E. - Wilkinson, L., (1986). An analityc approximation to the distribution of Lilliefors–s test statistic for normality. The American Statistician, vol. 40, n.4.Google Scholar
  7. Dancelli, L., (1986). Tendenza alia massima ed alia minima concentrazione nel modello di distribuzione del reddito di Dagum. Scritti in Onore di Francesco Brambilla, Vol. I, Università L. Bocconi, Milano.Google Scholar
  8. Gibbons. J.D., (1971). Non parametrical statistical inference, Mc Graw-Hill, New York. IMSL, (1987). Fortran Subroutines for statistical analysis, Houston.Google Scholar
  9. Latorre, G., (1987). Distribuzioni cionarie asintotiche di indici di concentrazione: approccio parametrico. Statistica, anno XLVII, n. 4.Google Scholar
  10. Latorre, G., (1988). Proprietà cionarie del modello di Dagum per la distribuzione dei redditi. Statistica, anno XLVIII, n.1.Google Scholar
  11. Lilliefors, H. W., (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, n. 63.Google Scholar
  12. Lilliefors, H. W., (1969). On the Kolmogorov-Smirnov test for exponential distribution with mean unknown. Journal of the American Statistical Association, n. 64.Google Scholar
  13. Mason, A. L. - Bell, C. B., (1986). New Lilliefors and Srinivasan tables with applications. Communications in Statistics-Simulations, vol. 15, n. 2.Google Scholar
  14. Pollastri, A., (1987). Characteristics of Zenga’s concentration index. AA. VV. La distribuzione personale del reddito: problemi di formazione, di ripartizione e di misurazione, a cura di M. Zenga, Vita e Pensiero, Milano.Google Scholar
  15. Rao, C. R., (1973). Linear Statistical inference and its applications, J. Wiley and Sons, New York.CrossRefGoogle Scholar
  16. Schmittlein, D. C., (1983). Some sling properties of a model for income distribution. Journal of Business & Economics Statistics, vol. 1, n. 1.CrossRefGoogle Scholar
  17. Singh, S. K., - Maddala, G. S., (1976). A function for size distribution of incomes.Econometrica, vol. 44, n. 5.CrossRefGoogle Scholar
  18. Zehna, P. W., (1966). Invariance of maximum likelihood estimation. Annals of Mathematical Statistics, vol. 37.Google Scholar
  19. Zenga, M., (a,1984). Tendenza alia massima ed alia minima concentrazione per variabili casuali continue.Statistica, anno XLIV, n. 4.Google Scholar
  20. Zenga, M., (b,1984). Proposta per un indice di concentrazione basato sui rapporti fra quantili di popolazione e quantili di reddito. Giornale degli Economisti ed Annali di Economia, Maggio - Giugno.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Giovanni Latorre
    • 1
  1. 1.Università degli Studi della CalabriaCosenzaItaly

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