Abstract
More than one hundred years after its introduction, Pareto’s proposed model for fitting income distributions continues to be heavily used. A variety of generalizations of this model have been proposed including discrete versions, together with natural multivariate extensions. Several stochastic scenarios can be used to justify the prevalence of income distributions exhibiting approximate Paretian behavior. This chapter will provide a survey of results related to these Pareto-like models including discussion of related distributional and inferential questions. Topics will include the classical Pareto models and its generalizations, stochastic income models leading to Paretian income distributions, distributional properties of generalized Pareto distributions, related discrete distributions, inequality measures for Paretian models, inferential issues and multivariate extensions.
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References
Arnold, B. C. (1983) Pareto Distributions, International Cooperative Publishing House, Fairland, Maryland USA.
Arnold, B. C., N. Balakrishnan and H. N. Nagaraja (1992) A First Course in Order Statistics, Wiley, New York.
Arnold, B. C., E. Castillo and J. M. Sarabia (1998) Bayesian Analysis for Classical Distributions Using Conditionally Specified Priors, Sankya B, 60, 228-245.
Arnold, B. C., E. Castillo and J. M. Sarabia (1999) Conditional Specification of Statistical Models, Springer, New York.
Arnold, B. C. and L. Laguna (1976) A Stochastic Mechanism Leading to Asymptotically Paretian Distributions, Proceedings of the American Statistical Association. Business and Economic Statistics Section.
Arnold, B. C. and L. Laguna (1977) On Generalized Pareto Distributions with Applications to Income Data, International Studies in Economics, Monograph No. 10, Department of Economics, Iowa State University.
Arnold, B. C. and S. J. Press (1986) Bayesian Analysis of Censored or Grouped Data from Pareto Populations, in Studies in Bayesian Econometrics and Statistics, 6, pp. 157-173, Amsterdam, North Holland.
Arnold, B. C. and S. J. Press (1989) Bayesian Estimation and Prediction for Pareto Data, Journal of American Statistical Association, 84, 1079-1084.
Balkema, A. A. and L. de Haan (1974) Residual Life Time at Great Age, Annals of Probability, 2, 792-804.
Brazauskas, V. (2002) Fisher Information Matrix for the Feller-Pareto Distribution, Statistics and Probability Letters, 59, 159-167.
Brazauskas, V. (2003) Information Matrix for Pareto (IV), Burr and Related Distri-butions, Communications in Statistics: Theory and Methods, 32, 315-325.
Brazauskas, V. and R. Serfling (2000) Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution, North American Actuarial Jour-nal, 4, 12-27.
Burr, I. W. (1942) Cumulative Frequency Functions, Annals of Mathematical Statistics, 13, 215-232.
Champernowne, D. G. (1937) The Theory of Income Distribution, Econometrica, 5, 379-381.
Champernowne, D. G. (1953) A Model of Income Distribution, Economic Journal, 63, 318-351.
Champernowne, D. G. (1973) The Distribution of Income, Cambridge University Press, Cambridge.
Dalton, H. (1920) The Measurement of the Inequality of Income, Economic Journal, 30, 348-361.
Ericson, O. (1945) Un Probleme de la Repartition des Revenus, Skand. Aktuar, 28, 247-257.
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, vol. 2, 2nd ed., Wiley, New York.
Gastwirth, J. L. (1971) A General Definition of the Lorenz Curve, Econometrica, 39, 1037-1039.
Gibrat, R. (1931) Les In égalit és E'conomiques, Librairie du Recueil Sirey, Paris.
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.
Houchens, R. L. (1984) Record Value Theory and Inference, Ph.D. Dissertation, University of California, Riverside, California.
Huang, J. S. (1978) On a “Lack of Memory” Property, Tech. Rep. 84, Statistical Series, University of Guelph, Guelph, Ontario, Canada.
Johnson, N. L., S. Kotz and N. Balakrishnan (1994) Continuous Univariate Distributions, vol. 1, 2nd ed., Wiley, New York.
Kalbfleisch, J. D. and R. L. Prentice (2002) The Statistical Analysis of Failure Time Data, 2nd ed., Wiley, New York.
Kleiber, C. and S. Kotz (2003) Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley, Hoboken, NJ.
Krishnaji, N. (1970) Characterization of the Pareto Distribution through a Model of Under-Reported Incomes, Econometrica, 38, 251-255.
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.
Lwin, T. (1972) Estimation of the Tail of the Paretian Law, Skand. Aktuar, 55, 170-178.
Lydall, H. F. (1959) The Distribution of Employment Income, Econometrica, 27, 110-115.
Mardia, K. V. (1962) Multivariate Pareto Distributions, Annals of Mathematical Statistics, 33, 1008-1015.
Pareto, V. (1897) Cours d’Economie Politique, Rouge, Lausanne.
Pickands, J. (1975) Statistical Inference Using Extreme Order Statistics, Annals of Statistics, 3, 119-131.
Pietra, G. (1932) Nuovi Contributi Alla Methodologia Degli Indici di Variabilita e di Concentrazione, Atti del Reale Instituto Veneto di Scienze, Lettere ed Arti, 91, 989-1008.
Pillai, R. N. (1991) Semi-Pareto Processes, Journal of Applied Probability, 28, 461-465.
Quandt, R. E. (1966) Old and New Methods of Estimation and the Pareto Distribution, Metrika, 10, 55-82.
Saksena, S. K. (1978) Estimation of Parameters in a Pareto Distribution and Simultaneous Comparison of Estimation, Ph.D. thesis, Louisiana Tech. University, Ruston (Louisiana).
Sukhatme, P. V. (1937) Tests of Significance for Samples of the Chi Squared Popu-lation with Two Degrees of Freedom, Annals of Eugenics, 8, 52-56.
Zipf, G. (1949) Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge.
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Arnold, B.C. (2008). Pareto and Generalized Pareto Distributions. In: Chotikapanich, D. (eds) Modeling Income Distributions and Lorenz Curves. Economic Studies in Equality, Social Exclusion and Well-Being, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72796-7_7
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DOI: https://doi.org/10.1007/978-0-387-72796-7_7
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