Comparaison de tendance centrale par l'analyse de transferts
Térouanne, Éric
Mathématiques et Sciences humaines, Tome 136 (1996), p. 63-76 / Harvested from Numdam
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La différence de tendance centrale entre deux distributions sur un ensemble fini est représentée par une série de transferts entre les modalités. Un modèle unique est proposé qui permet d'analyser ces différences pour des variables nominales, ordinales ou métriques aussi bien que pour les variables numériques. En particulier on définit un indice de différence entre les distributions qui se ramène à l'indice de distorsion de Gini dans le cas d'une variable nominale et à la différence entre les moyennes dans le cas d'une variable numérique.

Comparison of central tendencies by means of transfer analysis.The differences in the central tendency of two distributions on a finite set is represented by a series of transfers between modalities. A common model is presented which allows one to analyze these transfers for nominal, ordinal or metric variables, as well as for numerical ones. In particular, we define an index of difference between the distributions which boils down to Gini's distortion index in the case of a nominal variable and to the difference between the means in the case of a numerical variable.

@article{MSH_1996__134__63_0,
     author = {T\'erouanne, \'Eric},
     title = {Comparaison de tendance centrale par l'analyse de transferts},
     journal = {Math\'ematiques et Sciences humaines},
     volume = {136},
     year = {1996},
     pages = {63-76},
     zbl = {0865.62089},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/MSH_1996__134__63_0}
}

Térouanne, Éric. Comparaison de tendance centrale par l'analyse de transferts. Mathématiques et Sciences humaines, Tome 136 (1996) pp. 63-76. http://gdmltest.u-ga.fr/item/MSH_1996__134__63_0/

[1] Barbut M., "Sur quelques propriétés élémentaires des fonctions de concentration de C. Gini", Mathématiques, Informatique et Sciences humaines, 88 (1984), 5-19. | Numdam | Zbl 0556.62035

[2] Cifarelli D.M. et Regazzini E., "On a general definition of concentration function", Sankhya, 49 (B-3) (1987), 307-319. | MR 1056041 | Zbl 0647.62023

[3] Dalton H., "The measurement of the inequality of incomes", Econ. J., 30 (1920), 348-361.

[4] Gini C., "Sulla misura della concentrazione della variabilità dei caratteri", Atti del Reale Istituto Veneto di Sci., Litt., Arti, AA., 1913-1914, 73 (II) (1914), 1903-1942.

[5] Lorenz M.O., "Methods of measuring the concentration of wealth", Publ. Amer. Statist. Assoc., 9 (1905), 209-219.

[6] Marshall A.W. et Olkin J., Inequalities : theory of majorization and its applications, New York, Academic Press, 1979. | MR 552278 | Zbl 0437.26007

[7] Mosler K., "Majorization in economic disparity measures", Linear Algebra and its applications, 199 (1994), 91-114. | MR 1274409 | Zbl 0804.90005

[8] Mosler K. et Scarsini M., Stochastic orders and decision under risk, Hayward, California, IMS Lecture Notes - Monograph series (19), 1991. | MR 1196043 | Zbl 0745.00058

[9] Pigou A., Wealth and Welfare, New York, Macmillan, 1912.

[10] Regazzini E., "Concentration comparisons between probability measures", Sankhya, 54 (B) (1992), 129-149. | MR 1216304 | Zbl 0765.62021

[11] Térouanne E., "Distorsion entre deux distributions d'une variable nominale", Mathématiques, Informatique et Sciences humaines, 131 (1995), 29-38. | Numdam | Zbl 0847.62084

[12] Yitzhaki S. et Olkin I., "Concentration indices and concentration curves", in Stochastic ordrers and decision under risk, K. Mosler et M. Scarsini Eds., IMS Lecture Notes - Monograph series (19) (1991), 380-392. | MR 1196066 | Zbl 0755.90016