Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2010, Article ID 718905, 26 pages
http://dx.doi.org/10.1155/2010/718905
Research Article

Zenga's New Index of Economic Inequality, Its Estimation, and an Analysis of Incomes in Italy

1Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Università di Milano, Bicocca 20126, Milan, Italy
2Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada N6A 5B7

Received 2 October 2009; Accepted 28 February 2010

Academic Editor: Madan L. Puri

Copyright © 2010 Francesca Greselin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Zenga, “Inequality curve and inequality index based on the ratios between lower and upper arithmetic means,” Statistica & Applicazioni, vol. 5, pp. 3–27, 2007. View at Google Scholar
  2. G. Pietra, “Delle relazioni fra indici di variabilitá, note I e II,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, vol. 74, pp. 775–804, 1915. View at Google Scholar
  3. M. O. Lorenz, “Methods of measuring the concentration of wealth,” Journal of the American Statistical Association, vol. 9, pp. 209–219, 1905. View at Google Scholar
  4. C. Gini, “Sulla misura della concentrazione e della variabilità dei caratteri,” in Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. Anno Accademico, vol. 48, part 2, pp. 1201–1248, Premiate Officine Grafiche Carlo Ferrari, Venezia, Italy, 1914. View at Google Scholar
  5. V. Pareto, “La legge della domanda,” Giornale degli Economisti, vol. 10, pp. 59–68, 1895. View at Google Scholar
  6. V. Pareto, “Ecrits sur la courve de la répartition de la richesse,” in Complete Works of V. Pareto, G. Busino, Ed., Librairie Droz, Genève, Switzerland, 1965. View at Google Scholar
  7. M. Zenga, “Il contributo degli italiani allo studio della concentrazione,” in La Distribuzione Personale del Reddito: Problemi di Formazione, di Ripartizione e di Misurazione, M. Zenga, Ed., Vita e Pensiero, Milano, Italy, 1987. View at Google Scholar
  8. C. Dagum, “A new model of personal distribution: specification and estimation,” Economie Appliquée, vol. 30, pp. 413–437, 1977. View at Google Scholar
  9. C. Dagum, “The generation and distribution of income. The Lorenz curve and the Gini ratio,” Economie Appliquée, vol. 33, pp. 327–367, 1980. View at Google Scholar
  10. C. Dagum, “A model of net wealth distribution specified for negative, null and positive wealth. A case of study: Italy,” in Income and Wealth Distribution, Inequality and Poverty, C. Dagum and M. Zenga, Eds., pp. 42–56, Springer, Berlin, Germany, 1990. View at Google Scholar
  11. J. L. Gastwirth, “A general definition of the Lorenz curve,” Econometrica, vol. 39, pp. 1037–1039, 1971. View at Google Scholar
  12. F. Greselin and L. Pasquazzi, “Asymptotic confidence intervals for a new inequality measure,” Communications in Statistics: Simulation and Computation, vol. 38, no. 8, pp. 1742–1756, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. C. Kleiber and S. Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, Wiley Series in Probability and Statistics, Wiley-Interscience, Hoboken, NJ, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Z. A. Karian and E. J. Dudewicz, Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Method, CRC Press, Boca Raton, Fla, USA, 2000. View at MathSciNet
  15. B. L. Jones, M. L. Puri, and R. Zitikis, “Testing hypotheses about the equality of several risk measure values with applications in insurance,” Insurance: Mathematics & Economics, vol. 38, no. 2, pp. 253–270, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. V. Brazauskas, B. L. Jones, M. L. Puri, and R. Zitikis, “Nested L-statistics and their use in comparing the riskiness of portfolios,” Scandinavian Actuarial Journal, no. 3, pp. 162–179, 2007. View at Google Scholar · View at MathSciNet
  17. A. C. Davison and D. V. Hinkley, Bootstrap Methods and Their Application, vol. 1 of Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, UK, 1997. View at MathSciNet
  18. B. Efron, “Better bootstrap confidence intervals,” Journal of the American Statistical Association, vol. 82, no. 397, pp. 171–200, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Bank of Italy, “Household income and wealth in 2004,” Supplements to the Statistical Bulletin, Sample Surveys, vol. 16, no. 7, 2006. View at Google Scholar
  20. C. N. Chen, T. W. Tsaur, and T. S. Rhai, “The Gini coefficient and negative income,” Oxford Economic Papers, vol. 34, pp. 473–478, 1982. View at Google Scholar
  21. E. Maasoumi, “Empirical analysis of welfare and inequality,” in Handbook of Applied Econometrics, Volume II: Microeconomics, M. H. Pesaran and P. Schmidt, Eds., Blackwell, Oxford, UK, 1994. View at Google Scholar
  22. A. Necir, A. Rassoul, and R. Zitikis, “Estimating the conditional tail expectation in the case of heavy-tailed losses,” Journal of Probability and Statistics. In press. View at Publisher · View at Google Scholar
  23. R. Zitikis, “The Vervaat process,” in Asymptotic Methods in Probability and Statistics (Ottawa, ON, 1997), B. Szyszkowicz, Ed., pp. 667–694, North-Holland, Amsterdam, The Netherlands, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Y. Davydov and R. Zitikis, “Convex rearrangements of random elements,” in Asymptotic Methods in Stochastics, vol. 44 of Fields Institute Communications, pp. 141–171, American Mathematical Society, Providence, RI, USA, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. F. Greselin, M. L. Puri, and R. Zitikis, “L-functions, processes, and statistics in measuring economic inequality and actuarial risks,” Statistics and Its Interface, vol. 2, no. 2, pp. 227–245, 2009. View at Google Scholar · View at MathSciNet