Construction of concentration measures for general Lorenz curves using Riemann-Stieltjes integrals

Mathematical and Computer Modelling

Volumn 35, Issue 9-10, 2002, Pages 1149-1163

  Egghe, L ^a,b  

^a HASSELT UNIVERSITY   (Belgium)

^b UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Concentration measure; Lorenz curve; Riemann Stieltjes integral

Indexed keywords

DERIVATIVES; INTEGRAL EQUATIONS;

BIOMETRICS; LORENZ CURVES;

MATHEMATICAL TECHNIQUES;

EID: 4243148893     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(02)00077-8     Document Type: Article

References (27)

1. M.O. Lorenz, Methods of measuring concentration of wealth, Journal of the American Statistical Association 9, 209-219, (1905).
2. A. Sen, On Economic Inequality, Clarendon Press, Oxford, (1973).
3. P.D. Allison, Measures of inequality, American Sociological Review 43, 865-880, (1978).
4. H. Theil, Economics and Information Theory, North-Holland, Amsterdam, (1967).
5. R. Rousseau, Concentration and diversity in informetric research, Doctoral Thesis, University of Antwerp (UIA), Belgium (1992).
6. L. Egghe and R. Rousseau, Symmetric and asymmetric theory of relative concentration, Scientometrics 52 (2), 261-290, (2001).
7. T.M. Apostol, Mathematical Analysis. A Modern Approach to Advanced Calculus, Addison-Wesley, Reading, MA, (1957).
8. S.A. Douglas, Introduction to Mathematical Analysis, Addison-Wesley, Reading, MA, (1996).
9. G.H. Hardy, J.E. Littlewood and G. Pólya, Some simple inequalities satisfied by convex functions, Messenger of Mathematics 58, 145-152, (1928).
10. H.D. Brunk, On an inequality for convex functions, Proceedings of the American Mathematical Society 7, 817-824, (1956).
11. J.L. Gastwirth, A general definition of the Lorenz curve, Econometrica 39 (6), 1037-1039, (November 1971).
12. J.L. Gastwirth, The estimation of the Lorenz curve and Gini index, The Review of Economics and Statistics 54 (3), 306-316, (1972).
13. P.D. Thistle, Ranking distributions with generalized Lorenz curves, Southern Economic Journal 50 (1), 1-12, (1989).
14. M. Rothschild and J.E. Stiglitz, Some further results on the measurement of inequality, Journal of Economic Theory 6, 188-204, (1973).
15. S.M.R. Kanbur, The measurement and decomposition of inequality and poverty, In Mathematical Methods in Economics, Vol. 16, (Edited by F. van der Ploeg), pp. 403-432, J. Wiley and Sons, (1984).
16. G.P. Patil and C. Taillie, Diversity as a concept and its measurement, Journal of the American Statistical Association 77 (379), 548-561, (1982).
17. L. Egghe and R. Rousseau, Introduction to Informetrics. Quantitative Methods in Library, Documentation and Information Science, Elsevier, Amsterdam, (1990).
18. L. Egghe and R. Rousseau, Elements of concentration theory, In Proceedings of the Second International Conference on Bibliometrics, Scientometrics and Informetrics, London, Ontario, pp. 97-137, (1990).
19. A.B. Atkinson, On the measurement of inequality, Journal of Economic Theory 2, 244-263, (1970).
20. P.J. Lambert, Social welfare and the Gini coefficient revisited, Mathematical Social Sciences 9, 19-26, (1985).
21. T.M. Cover and J.A. Thomas, Elements of Information Theory, J. Wiley and Sons, New York, (1991).
22. S. Ihara, Information Theory for Continuous Systems, World Scientific, Singapore, (1993).
23. C.L. Viles and J.C. French, Content locality in distributed digital libraries, Information Processing and Management 35, 317-336, (1999).
24. R. Rousseau, Concentration and evenness measures as scientometric indicators, Preprint, (2000).
25. th International Conference on Research and Development in Information Retrieval (SIGIR), Brussels, pp. 469-493, (1990).
26. G. Salton and M.J. McGill, Introduction to Modern Information Retrieval, McGraw-Hill, Singapore, (1987).
27. L. Egghe and R. Rousseau, Comparing partial and truncated conglomerates from a concentration theoretic point of view, Preprint, (2001).