Fuzzy Monetary Poverty Measures under a Dagum Income Distributive Hypothesis

  • Gianni Betti
  • Antonella D’Agostino
  • Achille Lemmi
Part of the Economic Studies in Equality, Social Exclusion and Well-Being book series (EIAP, volume 5)


This chapter explores the potential of introducing the Dagum distribution into the IFR (Integrated Fuzzy Relative) poverty measure. This implies using the Dagum model for fitting the empirical cumulative distribution that forms one of the components of the membership function to the set of poor in the IFR methodology. Moreover, we propose a heterogeneous Dagum model in order to allow the form of income distribution to vary with personal characteristics. In this way, we are able to make comparisons across sub-groups of the population between the traditional and the IFR measures of poverty.


Income Distribution Poverty Line Lorenz Curve Poverty Measure Wealth Distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aitchison, J. and J. A. C. Brown (1957) The Lognormal Distribution with Special References to Its Uses in Economics, Cambridge University Press, Cambridge. Google Scholar
  2. Baliamoune-Lutz, M. (2006) On the Measurement of Human Well-being: Fuzzy-set Theory and Sen’s Capability Approach, in M. McGillivray and M. Clarke (eds.) Understanding Human Well-being, pp. 119-138, Brooking Institution Press, Washington D.C.Google Scholar
  3. Berenger, V. and A. Verdier-Chouchane (2007) Multidimensional Measures of Well-Being: Standard of Living and Quality of Life Across Countries, World Development, 35, 1259-1276.CrossRefGoogle Scholar
  4. Betti, G., B. Cheli and R. Cambini (2004) A Statistical Model for the Dynamics be-tween Two Fuzzy States: Theory and an Application to Poverty Analysis, Metron, 62, 391-411.Google Scholar
  5. Betti, G., B. Cheli, A. Lemmi and V. Verma (2006) Multidimensional and Longitudi-nal Poverty: an Integrated Fuzzy Approach, in A. Lemmi and G. Betti (eds.) Fuzzy Set Approach to Multidimensional Poverty Measurement, pp. 111-137, Springer, New York.Google Scholar
  6. Betti, G. and V. Verma (1999) Measuring the Degree of Poverty in a Dynamic and Comparative Context: A Multi-dimensional Approach Using Fuzzy Set Theory, Proceedings ICCS-VI, 11:289-301, Lahore, Pakistan.Google Scholar
  7. Betti, G. and V. Verma (2008) Fuzzy Measures of the Incidence of Relative Poverty and Deprivation: A Multi-dimensional Perspective, Statistical Methods and Applications, forthcoming.Google Scholar
  8. Biewen, M. and S. P. Jenkins (2005) A Framework for the Decomposition of Poverty Differences with an Application to Poverty Differences between Countries, Empirical Economics, 30, 331-358.CrossRefGoogle Scholar
  9. Botargues, P. and D. Petrecolla (1999) Estimaciones Param étricas y no Param étricas de la Distribuci ón del Ingreso de los Ocupados del Gran Buenos Aires, 1992-1997, Economica (National University of La Plata), 45.Google Scholar
  10. Burr, I. W. (1942) Cumulative Frequency Functions, Annals of Mathematical Statistics, 13, 215-232.CrossRefGoogle Scholar
  11. Cerioli, A. and S. Zani (1990) A Fuzzy Approach to the Measurement of Poverty, in C. Dagum and M. Zenga (eds.) Income and Wealth Distribution, Inequality and Poverty, Studies in Contemporary Economics, pp. 272-284, Springer, Berlin.Google Scholar
  12. Cheli, B. (1995a) Totally Fuzzy and Relative Measures in Dynamic Context, Metron, 53, 183-205.Google Scholar
  13. Cheli, B. (1995b) Totally Fuzzy and Relative Measures of Poverty in Dynamic Context. An Application to the British Households Panel Survey, ISER Work-ing Papers, 1995-95-13. Institute for Social and Economic Research, University of Essex, Colchester, UK.Google Scholar
  14. Cheli, B. and G. Betti (1999) Fuzzy Analysis of Poverty Dynamics on an Italian Pseudo Panel, 1985-1994, Metron, 57, 83-103.Google Scholar
  15. Cheli, B. and A. Lemmi (1995) A Totally Fuzzy and Relative Approach to Multidimensional Analysis of Poverty, Economic Notes, 24, 115-134.Google Scholar
  16. Chiappero, M. E. (2000) A Multidimensional Assessment of Well-being Based on Sen’s Functioning Approach, Rivista Internazionale di Scienze Sociali, 108, 207-239. Google Scholar
  17. Cox, D. R. and E. J. Snell (1968) A General Definition of Residuals, Journal of the Royal Statistical Society, Series B (Methodological), 30, 248-275.Google Scholar
  18. Dagum, C. (1973) Un Mod èle non Lin éaire de R épartition Fonctionnelle du Revenu, Economie Appliqu ée, 26, 843-876.Google Scholar
  19. Dagum, C. (1975) A Model of Income Distribution and the Conditions of Existence of Moments of Finite Order, Proceedings of the 40th Session of the International Statistical Institute, Vol. XLVI, Book 3, Warsaw, pp 199-205.Google Scholar
  20. Dagum, C. (1977) A New Model of Personal Income Distribution: Specification and Estimation, Economie Appliqu ée, 30, 413-436.Google Scholar
  21. Dagum, C. (1980a) Inequality Measures between Income Distributions with Applications, Econometrica, 48, 1791-1803.CrossRefGoogle Scholar
  22. Dagum, C. (1980b) The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Appliqu ée, 33, 327-367.Google Scholar
  23. Dagum, C. (1983) Medida de la Deferencial del Ingreso Entre Familias Blancas, Negras y de Origen Hipanico en los Estados Unidos, El Trimestre Economico, 50 (2).Google Scholar
  24. Dagum, C. (1990) A Model of Net Wealth Distribution Specified for Negative, Null and Positive Wealth. A Case Study: Italy, in C. Dagum and M. Zenga (eds.) Income and Wealth Distribution, Inequality and Poverty, pp. 42-56, Spinger-Verlag, Berlin, Heidelberg.Google Scholar
  25. Dagum, C. and M. Costa (2004) Analysis and Measurement of Poverty. Univariate and Multivariate Approaches and Their Policy Implications. A Case Study: Italy, in C. Dagum and G. Ferrari (eds.) Household Behaviour, Equivalence Scales, Welfare and Poverty, pp. 221-272, Physica-Verlag, Heidelberg.Google Scholar
  26. Dagum, C., R. Gambassi and A. Lemmi (1992) New Approaches to the Measure-ment of Poverty, in Poverty Measurement for Economies in Transition in Eastern European Countries, Warsaw: Polish Statistical Association and Central Statistical Office, pp. 201-225.Google Scholar
  27. Dagum, C. and A. Lemmi (1989) A Contribution to the Analysis of Income Distribution and Income Inequality and a Case Study: Italy, in D. J. Slottje (ed.) Advances in Econometrics, pp. 123-157, JAI Press, Greenwich, CT.Google Scholar
  28. Dastrup, S. R., R. Hartshorn and J. B. McDonald (2007) The Impact of Taxes and Transfer Payments on the Distribution of Income: A Parametric Comparison, Journal of Economic Inequality, 5, 353-369.CrossRefGoogle Scholar
  29. Dubois, D. and H. Prade (1980) Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.Google Scholar
  30. Fattorini, L. and A. Lemmi (1979) Proposta di un Modello Alternativo per l’Analisi della Distribuzione Personale del Reddito, atti delle Giornate di Lavoro AIRO, Bologna, pp. 89-117.Google Scholar
  31. Kleiber, C. (1996) Dagum vs. Singh-Maddala Income Distributions, Economic Letters, 53, 265-268.CrossRefGoogle Scholar
  32. Lelli, S. (2001) Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influ-ence of Different Techniques on Sen’s Functioning Approach, Discussion Paper Series DPS 01.21, Center for Economic Studies, Catholic Univeristy of Leuven, Belgium.Google Scholar
  33. Lemmi, A. and G. Betti (2006) Fuzzy Set Approach to Multidimensional Poverty Measurement, Springer, New York.CrossRefGoogle Scholar
  34. McGillivray, M. and M. Clarke (2006) Understanding Human Well-being, Brooking Institution Press, Washington D.C.CrossRefGoogle Scholar
  35. Pudney, S. (1999) On Some Statistical Methods for Modelling the Incidence of Poverty, Oxford Bulletin of Economics and Statistics, 61, 385–408.CrossRefGoogle Scholar
  36. Qizilbash, M. (2003) Vague Language and Precise Measurement: The Case of Poverty, Journal of Economic Methodology, 10, 41–58.CrossRefGoogle Scholar
  37. Quintano, C. and A. D’Agostino (2006) Studying Inequality in Income Distribution of Single Person Household in Four Developed Countries, Review of Income and Wealth, 52, 525–546.CrossRefGoogle Scholar
  38. Rojas, M. (2006) Well-being and the Complexity of Poverty: A Subjective Wellbeing Approach, in M. McGillivray and M. Clarke (eds.) Understanding Human Well-being, pp. 182–206, Brooking Institution Press, Washington D.C.Google Scholar
  39. Ruggeri, L. C., R. Saith and F. Stewart (2006) Does it Matter that We do not Agree on the Definition of Poverty? A Comparison of Four Approaches, in M. McGillivray and M. Clarke (eds.) Understanding Human Well-being, pp. 19–53, Brooking Institution Press, Washington D.C.Google Scholar
  40. Salem, A. B. and T. D. Mount (1974) A Convenient Descriptive Model of Income Distribution: The Gamma Density, Econometrica, 42, 1115–1127.CrossRefGoogle Scholar
  41. Singh, S. K. and G. S. Maddala (1976) A Function for Size Distribution of Incomes, Econometrica, 44(5), 963–970.CrossRefGoogle Scholar
  42. Tadikamalla, P. R. (1980) A Look at the Burr and Related Distributions, International Statistical Review, 48, 337–344.CrossRefGoogle Scholar
  43. Verma, V. and G. Betti (2006) EU Statistics on Income and Living Conditions (EUSILC): Choosing the Survey Structure and Sample Design, Statistics in Transition, 7, 935–970.Google Scholar
  44. Zadeh, L. A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Gianni Betti
    • 1
  • Antonella D’Agostino
    • 2
  • Achille Lemmi
    • 1
  1. 1.Research Centre on Income Distribution “C. Dagum”University of SienaItaly
  2. 2.Department of Statistics and Mathematics for the Economic ResearchUniversity of Naples “Parthenope”NaplesItaly

Personalised recommendations