Skip to main content

Advertisement

Log in

A vector valued bivariate gini index for truncated distributions

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Gini index is widely used in the study of inequality of income distribution. In the present paper we give a definition of the Gini index in the Bivariate set-up and look into the problem of characterizing probability distributions based on some relationship between this index and various other commonly used measures. We also generalized the Gini index to a situation where several attributes of the population are considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson J M (1999) The wealth of U.S.families, Analysis of recent census data. Capital Research Associates. 233, 1–45

    Google Scholar 

  2. Arnold B C (1987) Majorization and the Lorenz Order, A Brief Introduction. Springer, Berlin

    MATH  Google Scholar 

  3. Atkinson A B Bourguignon F (1982) The Comparison of Multidimensioned Dimensioned Distributions of Economic Status. Review of Economic Studies 49, 183–201

    Article  Google Scholar 

  4. Atkinson A B, Bourguignon F (1989) The Design of Direct Taxation and Family Benefits. Journal of Public Economics 41, 3–29

    Article  Google Scholar 

  5. Geetha K G Nair V K R (1998) A family of Bivariate distribution useful in Reliability Modelling, Statistical Methods in Quality and Reliability. Educational Publishers and distributors, New Delhi, 50–58.

    Google Scholar 

  6. Gumbel E J (1960) Bivariate exponential distribution. Journal of the American Statistical Association 55, 698–707

    Article  MATH  Google Scholar 

  7. Kolm S C (1977) Multidimensional Egalitarianisms. Quarterly Journal of Economics 91, 1–13

    Article  MATH  Google Scholar 

  8. Koshevoy G, Mosler K (1996) The Lorenz Zonoid of a Multivariate Distribution. Journal of the American Statistical Association 91, 873–882

    Article  MATH  Google Scholar 

  9. Koshevoy G, Mosler K (1997) Multivariate Gini indices. Journal of Multivariate Analysis 60, 252–276

    Article  MATH  Google Scholar 

  10. Massoumi E (1986) The Measurement and Decomposition of Multi Dimensional Inequality. Econometrica 54, 991–997

    Article  Google Scholar 

  11. Massoumi E, Nickelsburg G (1988), Multivariate Measures of well-being and an Analysis of Inequality in the Michigan Data. Journal of Business and Economic Statistics 6, 327–334

    Article  Google Scholar 

  12. Mosler K (1994a) Multidimensional Welfarisms in Models and Measurement of Inequality and Welfare. ed W Eichhorn, Springer Berlin, 808–820

    Google Scholar 

  13. Nair N U, Nair V K R (1988), A characterization of the Bivariate exponential distribution. Biometric Journal 30,107–112

    Article  MATH  Google Scholar 

  14. Ord J K, Patil G P and Taillie (1983), Truncated Distributions and measures of income inequality. Sankhya: The Indian journal of Statistics, Ser B 413–430.

  15. Rietveld P (1990) Multidimensional Inequality Comparisons. Economics Letters, 32, 187–192

    Article  Google Scholar 

  16. Sankaran P G, Nair N U (1991) On Bivariate vitality functions. Proceedings of National Symposium on Distribution theory

  17. Sankaran P G, Nair N U (1993) A Bivariate Pareto Model and Its Applications to Reliability. Naval Research Logistics, 40, 1013–1020

    Article  MATH  Google Scholar 

  18. Sankaran P G, Nair N U (1996) On a Bivariate finite range distribution. Journal of Indian Statistical Association, 34, 119–124

    Google Scholar 

  19. Slottje D J (1987) Relative Price Changes and Inequality in the Size Distribution of Various Components. Journal of business and Economic Statistics 5, 19–26

    Article  Google Scholar 

  20. Sen P K (1988) The harmonic Gini coefficient and affluence indexes. Mathematical Social Sciences, 16, 65–76

    Article  MATH  Google Scholar 

  21. Taguchi T (1972a) On the Two-Dimensional Concentration Surface and Extensions of Concentration Coefficient and Pareto Distribution to the Two-Dimensional Case-I. Annals of the Institute of Statistical Mathematics, 24, 355–382

    Article  MATH  Google Scholar 

  22. Taguchi T (1972b) On the Two-Dimensional Concentration Surface and Extensions of Concentration Coefficient and Pareto Distribution to the Two-Dimensional Case-II. Annals of the Institute of Statistical Mathematics, 24, 599–619

    Article  MATH  Google Scholar 

  23. Taguchi T (1981) On a multiple Gini’s coefficient and some concentrative regressions. Metron, 1, 69–98

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abdul-Sathar, E.I., Suresh, R.P. & Nair, K.R.M. A vector valued bivariate gini index for truncated distributions. Statistical Papers 48, 543–557 (2007). https://doi.org/10.1007/s00362-007-0356-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-007-0356-1

Key words

Navigation