In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.


Income Inequality Income Distribution Stochastic Dominance Lorenz Curve Wealth Distribution 
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  1. Atkinson, A. B. (1970) On the Measurement of Inequality, Journal of Economic Theory, 2, 244-263.CrossRefGoogle Scholar
  2. Azzalini, A. T., T. dal Cappello and S. Kotz (2003) Log-skew-normal and Logskew-t Distributions as Models for Family Income Data, Journal of Income Distribution, 11, 12-20.Google Scholar
  3. Bandourian, R., J. B. McDonald and R. S. Turley (2003) A Comparison of Paramet-ric Models of Income Distribution across Countries and over Time, Estadística, 55, 135-152.Google Scholar
  4. Bantilan, M. C. S., N. B. Bernal, M. M. de Castro and J. M. Pattugalan (1995) In-come Distribution in the Philippines, 1957-1988: An Application of the Dagum Model to the Family Income and Expenditure Survey (FIES) Data, in C. Dagum and A. Lemmi (eds.) Research on Economic Inequality, Vol. 6: Income Distribu-tion, Social Welfare, Inequality and Poverty, Greenwich, CT: JAI Press, 11-43. Google Scholar
  5. 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
  6. Blayac, T. and D. Serra (1997) Tarifs Publics et Redistribution Spatiale. Une appli-cation aux Transports Ferroviaires, Revue d’Economie R égionale et Urbaine, 4, 603-618.Google Scholar
  7. Bordley, R. F., J. B. McDonald and A. Mantrala (1996) Something New, Something Old: Parametric Models for the Size Distribution of Income, Journal of Income Distribution, 6, 91-103.Google Scholar
  8. Botargues, P. and D. Petrecolla (1999a) Funciones de Distribuci ón del Ingreso y Afluencia Econ ómica Relativa para Ocupados Seg ún nivel de Educaci ón en GBA, Argentina, 1992-1996, in M. Cardenas Santa Maria and N. Lustig (eds.) Pobreza y desigualdad en Am érica Latina, Santaf é de Bogot á , D.C., Fedesarrollo, Lacea, Colciencias, Tercer Mundo. Also Documento de Trabajo Instituto Torcuato Di Tella, DTE 216.Google Scholar
  9. Botargues, P. and D. Petrecolla (1999b) 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), XLV (No 1), 13-34.Google Scholar
  10. Burr, I. W. (1942) Cumulative Frequency Functions, Annals of Mathematical Statistics, 13, 215-232.CrossRefGoogle Scholar
  11. Campano, F. (1991) Recent Trends in US Family Income Distribution: A Compari-son of All, White, and Black Families, Journal of Post-Keynesian Economics, 13, 337-350.Google Scholar
  12. Cheli, B., A. Lemmi and C. Spera (1995) An EM Algorithm for Estimating Mixtures of Dagum’s Models, in C. Dagum and A. Lemmi (eds.) Research on Economic Inequality, Vol. 6: Income Distribution, Social Welfare, Inequality and Poverty, Greenwich, CT: JAI Press, 131-142.Google Scholar
  13. Chotikapanich, D. and W. E. Griffiths (2006) Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions, in J. Creedy and G. Kalb (eds.) Research on Economic Inequality, Vol 13: Dynamics of Inequality and Poverty, pp. 297-321, Elsevier, Amsterdam.Google Scholar
  14. Clark, R. M., S. J. D. Cox and G. M. Laslett (1999) Generalizations of Power-law Distributions Applicable to Sampled Fault-trace Lengths: Model Choice, Param-eter Estimation and Caveats, Geophysical Journal International, 136, 357-372.CrossRefGoogle Scholar
  15. Cowell, F. A. and M.-P. Victoria-Feser (2006) Distributional Dominance with Trimmed Data, Journal of Business & Economic Statistics, 24, 291-300.CrossRefGoogle Scholar
  16. D’Addario, R. (1949) Richerche sulla Curva dei Redditi, Giornale degli Economisti e Annali di Economia, 8, 91-114.Google Scholar
  17. Dagum, C. (1975) A Model of Income Distribution and the Conditions of Existence of Moments of Finite Order, Bulletin of the International Statistical Institute, 46, 199-205, Proceedings of the 40th Session of the ISI, Warsaw, Contributed Papers.Google Scholar
  18. Dagum, C. (1977) A New Model for Personal Income Distribution: Specification and Estimation, Economie Appliqu ée, 30, 413-437. Google Scholar
  19. Dagum, C. (1980a) Generating Systems and Properties of Income Distribution Models, Metron, 38, 3-26.Google Scholar
  20. Dagum, C. (1980b) Sistemas Generadores de Distribuci ón de Ingreso y la ley de Pareto, El Trimestre Economico, 47, 877-917, reprinted in Estadística, 35 (1981), 143-183.Google Scholar
  21. Dagum, C. (1980c) The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Appliqu ée, 33, 327-367.Google Scholar
  22. Dagum, C. (1983) Income Distribution Models, in S. Kotz, N. L. Johnson and C. Read (eds.) Encyclopedia of Statistical Sciences, vol. 4, John Wiley, New York.Google Scholar
  23. Dagum, C. (1985) Analysis of Income Distribution and Inequality by Education and Sex in Canada, in R. L. Basmann and G. F. Rhodes, Jr (eds.) Advances in Econometrics, vol. 4, pp. 167-227.Google Scholar
  24. Dagum, C. (1990) Generation and Properties of Income Distribution Function, in C. Dagum and M. Zenga (eds.) Income and Wealth Distribution, Inequality and Poverty: Proceedings of the Second International Conference on Income Distribution by Size: Generation, Distribution, Measurement and Applications., pp. 1-17, Springer, New York - Berlin - London - Tokyo.Google Scholar
  25. Dagum, C. (1996) A Systemic Approach to the Generation of Income Distribution Models, Journal of Income Distribution, 6, 105-126.Google Scholar
  26. Dagum, C. (1999) Linking the Functional and Personal Distributions of Income, in J. Silber (ed.) Handbook on Income Inequality Measurement, pp. 101-128, Kluwer, Boston - Dordrecht - London.Google Scholar
  27. Dagum, C. and K. Chiu (1991) Users Manual for the Program “EPID” (Econo-metric Package for Income Distribution) for Personal Computers. Statistics Canada/Statistique Canada: Time Series Research and Analysis Division.Google Scholar
  28. Dagum, C., F. Guibbaud-Seyte and M. Terraza (1995) Analyse Interr égionale des Distributions des Salaires Français, Economie Appliqu ée, 48, 103-133.Google Scholar
  29. Dagum, C. and A. Lemmi (1989) A Contribution to the Analysis of Income Dis-tribution and Income Inequality and a Case Study: Italy, Research on Economic Inequality, 1, 123-157.Google Scholar
  30. Dagum, C. and D. J. Slottje (2000) A New Method to Estimate the Level and Distribution of Household Human Capital with Application, Structural Change and Economic Dynamics, 11, 67-94.CrossRefGoogle Scholar
  31. Dancelli, L. (1986) Tendenza alla Massima ed alla Minima Concentrazione nel Modello di Distribuzione del Reddito Personale di Dagum, in Scritti in Onore di Francesco Brambilla, vol. 1, Ed. Bocconi Comunicazioni, Milano, 249-267.Google Scholar
  32. Doma nski, C. and A. Jedrzejczak (1998) Maximum Likelihood Estimation of the Dagum Model Parameters, International Advances in Economic Research, 4, 243-252.CrossRefGoogle Scholar
  33. Doma nski, C. and A. Jedrzejczak (2002) Income Inequality Analysis in the Period of Economic Transformation in Poland, International Advances in Economic Research, 8, 215-220.CrossRefGoogle Scholar
  34. Domma, F. (1997) Mediana e Range Campionario per il Modello di Dagum, Quaderni di Statistica e Matematica Applicata alle Scienze Economico-Sociali, 19, 195-204.Google Scholar
  35. Domma, F. (2002) L’andamento della Hazard Function nel Modello di Dagum a tre Parametri, Quaderni di Statistica, 4, 1-12.Google Scholar
  36. Espinguet, P. and M. Terraza (1983) Essai d’Extrapolation des Distributions de Salaires Français, Economie Appliqu ée, 36, 535-561.Google Scholar
  37. Falc ão Carneiro, J. (1982) Modelo de Dagum de Distribuiç ão Pessoal do Rendi-mento: Uma Aplicaç ão às Receitas Familiares em Portugal, An álise Social, 18, 231-243.Google Scholar
  38. Fattorini, L. and A. Lemmi (1979) Proposta di un modello Alternativo per L’analisi della Distribuzione Personale del Reddito, Atti Giornate di Lavoro AIRO, 28, 89-117.Google Scholar
  39. Fisk, P. R. (1961) The Graduation of Income Distributions, Econometrica, 29, 171-185.CrossRefGoogle Scholar
  40. Gibrat, R. (1931) Les In égalit és E'conomiques, Librairie du Recueil Sirey, Paris.Google Scholar
  41. Gini, C. (1914) Sulla Misura della Concentrazione e della Variabilit à dei Caratteri, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 73, 1203-1248.Google Scholar
  42. Glomm, G. and B. Ravikumar (1998) Opting out of Publicly Provided Services: A Majority Voting Result, Social Choice and Welfare, 15, 187-199.CrossRefGoogle Scholar
  43. Hasegawa, H. and H. Kozumi (2003) Estimation of Lorenz Curves: A Bayesian Nonparametric Approach, Journal of Econometrics, 115, 277-291.CrossRefGoogle Scholar
  44. Jenkins, S. P. (1999) Fitting Singh-Maddala and Dagum Distributions by Maximum Likelihood, in Stata Technical Bulletin, 48, 19-25, also in Stata Technical Bulletin Reprints, vol. 8, 261-268. College Station, TX: Stata Press.Google Scholar
  45. Jenkins, S. P. (2007) Inequality and the GB2 Income Distribution. Working Paper 2007-12. Colchester: Institute for Social and Economic Research, University of Essex.Google Scholar
  46. Jenkins, S. P. and M. J äntti (2005) Methods for Summarizing and Comparing Wealth Distributions, ISER Working Paper 2005-05. Colchester: University of Essex, Institute for Social and Economic Research.Google Scholar
  47. Kleiber, C. (1996) Dagum vs. Singh-Maddala Income Distributions, Economics Letters, 53, 265-268.CrossRefGoogle Scholar
  48. Kleiber, C. (1999) On the Lorenz Order within Parametric Families of Income Distributions, Sankhya¯ B, 61, 514-517.Google Scholar
  49. Kleiber, C. (2007) On the Zenga Order within Parametric Families of Income Distributions, Working paper, Universit ät Basel, Switzerland.Google Scholar
  50. Kleiber, C. (2008) The Lorenz Curve in Economics and Econometrics, in G. Betti and A. Lemmi (eds.) Advances on Income Inequality and Concentration Mea-sures. Collected Papers in Memory of Corrado Gini and Max O. Lorenz, Routledge, London.Google Scholar
  51. Kleiber, C. and S. Kotz (2003) Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley, Hoboken, NJ.CrossRefGoogle Scholar
  52. Klonner, S. (2000) The First-Order Stochastic Dominance Ordering of the SinghMaddala Distribution, Economics Letters, 69, 123-128.CrossRefGoogle Scholar
  53. Kotz, S., N. L. Johnson and C. Read (eds.) (1983) Encyclopedia of Statistical Sciences, vol. 4, John Wiley, New York.Google Scholar
  54. Latorre, G. (1988) Propriet à Campionarie del Modello di Dagum per la Distribuzione dei Redditi, Statistica, 48, 15-27.Google Scholar
  55. Lorenz, M. O. (1905) Methods of Measuring the Concentration of Wealth, Quarterly Publications of the American Statistical Association, 9 (New Series, No. 70), 209-219.Google Scholar
  56. Łukasiewicz, P. and A. Orłowski (2004) Probabilistic Models of Income Distributions, Physica A, 344, 146-151.CrossRefGoogle Scholar
  57. Majumder, A. and S. R. Chakravarty (1990) Distribution of Personal Income: Development of a New Model and Its Application to US Income Data, Journal of Applied Econometrics, 5, 189-196.CrossRefGoogle Scholar
  58. Martín Reyes, G., A. Fern ández Morales and E. B árcena Martí (2001) Estimaci ón de una Funci ón Generadora de la Renta Mediante un Modelo de Variables Latentes, Estadística Espa ñola, 43, 63-87.Google Scholar
  59. McDonald, J. B. (1984) Some Generalized Functions for the Size Distribution of Income, Econometrica, 52, 647-663.CrossRefGoogle Scholar
  60. McDonald, J. B. and A. Mantrala (1995) The Distribution of Income: Revisited, Journal of Applied Econometrics, 10, 201-204.CrossRefGoogle Scholar
  61. McDonald, J. B. and Y. J. Xu (1995) A Generalization of the Beta Distribution with Applications, Journal of Econometrics, 66, 133-152, Erratum: Journal of Econometrics, 69: 427-428.Google Scholar
  62. Mielke, P. W. (1973) Another Family of Distributions for Describing and Analyzing Precipitation Data, Journal of Applied Meteorology, 12, 275-280.CrossRefGoogle Scholar
  63. Mielke, P. W. and E. S. Johnson (1974) Some Generalized Beta Distributions of the Second Kind having Desirable Application Features in Hydrology and Meteorology, Water Resources Research, 10, 223-226.CrossRefGoogle Scholar
  64. Palmitesta, P., C. Provasi and C. Spera (1999) Approximated Distributions of Sam-pling Inequality Indices, Computational Economics, 13, 211-226.CrossRefGoogle Scholar
  65. Palmitesta, P., C. Provasi and C. Spera (2000) Confidence Interval Estimation for Inequality Indices of the Gini Family, Computational Economics, 16, 137-147.CrossRefGoogle Scholar
  66. Panjer, H. H. (2006) Operational Risks, John Wiley, Hoboken, NJ.CrossRefGoogle Scholar
  67. Pareto, V. (1895) La Legge della Domanda, Giornale degli Economisti, 10, 59-68. English Translation in Rivista di Politica Economica, 87 (1997), 691-700 .Google Scholar
  68. Pareto, V. (1896) La Courbe de la R épartition de la Richesse, Reprinted 1965 in G. Busoni (ed.): Œeuvres Compl ètes de Vilfredo Pareto, Tome 3: E'crits sur la Courbe de la R épartition de la Richesse, Geneva: Librairie Droz. English translation in Rivista di Politica Economica, 87 (1997), 645-700.Google Scholar
  69. Pareto, V. (1897) Cours d’Economie Politique, Rouge, Lausanne.Google Scholar
  70. Pocock, M. L., J. B. McDonald and C. L. Pope (2003) Estimating Faculty Salary Distributions: An Application of Order Statistics, Journal of Income Distribution, 11, 43-51.Google Scholar
  71. Polisicchio, M. (1990) Sulla Interpretazione dei Parametri di Modelli Analitici per la Distribuzione del Reddito Personale, Statistica, 50, 383-397.Google Scholar
  72. Quintano, C. and A. D’Agostino (2006) Studying Inequality in Income Distribution of Single-Person Households in Four Developed Countries, Review of Income and Wealth, 52, 525-546.CrossRefGoogle Scholar
  73. R Development Core Team (2007) R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
  74. Rodriguez, R. N. (1983) Burr Distributions, in S. Kotz and N. L. Johnson (eds.) Encyclopedia of Statistical Sciences, Vol 1, 335-340, John Wiley, New York.Google Scholar
  75. Saposnik, R. (1981) Rank Dominance in Income Distributions, Public Choice, 36, 147-151.CrossRefGoogle Scholar
  76. Shao, Q. (2002) Maximum Likelihood Estimation for Generalised Logistic Distributions, Communications in Statistics: Theory and Methods, 31, 1687-1700.CrossRefGoogle Scholar
  77. Singh, S. K. and G. S. Maddala (1976) A Function for the Size Distribution of Incomes, Econometrica, 44, 963-970.CrossRefGoogle Scholar
  78. Stoppa, G. (1995) Explicit Estimators for Income Distributions, in C. Dagum and A. Lemmi (eds.) Research on Economic Inequality, Vol. 6: Income Distribution, Social Welfare, Inequality and Poverty, Greenwich, CT: JAI Press, 393-405.Google Scholar
  79. Tadikamalla, P. R. (1980) A Look at the Burr and Related Distributions, International Statistical Review, 48, 337-344.CrossRefGoogle Scholar
  80. Venables, W. N. and B. D. Ripley (2002) Modern Applied Statistics with S, 4th ed., Springer, New York.Google Scholar
  81. Victoria-Feser, M.-P. (1995) Robust Methods for Personal Income Distribution Models with Applications to Dagum’s Model, in C. Dagum and A. Lemmi (eds.) Research on Economic Inequality, Vol. 6: Income Distribution, Social Welfare, Inequality and Poverty, Greenwich, CT: JAI Press, 225-239.Google Scholar
  82. Victoria-Feser, M.-P. (2000) Robust Methods for the Analysis of Income Distribution, Inequality and Poverty, International Statistical Review, 68, 277-293.Google Scholar
  83. Yee, T. W. (2007) VGAM: Vector Generalized Linear and Additive Models, R pack-age version 0.7-5.∼yee/VGAM.
  84. Zelterman, D. (1987) Parameter Estimation in the Generalized Logistic Distribution, Computational Statistics & Data Analysis, 5, 177-184.CrossRefGoogle Scholar
  85. Zenga, M. (1984) Proposta per un Indice di Concentrazione Basato sui Rapporti fra Quantili di Popolazione e Quantili di Reddito, Giornale degli Economisti e Annali di Economia, 48, 301-326.Google Scholar

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Authors and Affiliations

  1. 1.Dept. of Statistics and EconometricsUniversität BaselBaselSwitzerland

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