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Ubeda-Flores, Manuel. (1401). A Note on the Maximum Difference Between Schweizer and Wolff's $\sigma$ and the Absolute Value of Spearman's $\rho$. نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 1(2), 1-5. doi: 10.30495/tfss.2022.1956899.1024
Manuel Ubeda-Flores. "A Note on the Maximum Difference Between Schweizer and Wolff's $\sigma$ and the Absolute Value of Spearman's $\rho$". نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 1, 2, 1401, 1-5. doi: 10.30495/tfss.2022.1956899.1024
Ubeda-Flores, Manuel. (1401). 'A Note on the Maximum Difference Between Schweizer and Wolff's $\sigma$ and the Absolute Value of Spearman's $\rho$', نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 1(2), pp. 1-5. doi: 10.30495/tfss.2022.1956899.1024
Ubeda-Flores, Manuel. A Note on the Maximum Difference Between Schweizer and Wolff's $\sigma$ and the Absolute Value of Spearman's $\rho$. نشریه علمی پژوهشی دانشگاه آزاد اسلامی, 1401; 1(2): 1-5. doi: 10.30495/tfss.2022.1956899.1024

A Note on the Maximum Difference Between Schweizer and Wolff's $\sigma$ and the Absolute Value of Spearman's $\rho$

Transactions on Fuzzy Sets and Systems
مقاله 2، دوره 1، شماره 2، بهمن 2022، صفحه 1-5    اصل مقاله (243.33 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.30495/tfss.2022.1956899.1024
نویسنده
Manuel Ubeda-Flores*
Department of Mathematics, University of Almer´ıa, 04120 Almer´ıa, Spain.
چکیده
In this note we correct an error on the possible maximum difference between the (measure of dependence) Schweizer and Wolff's sigma and the absolute value of the (measure of concordance) Spearman's rho given in [B. Schweizer and E. F. Wolff, On nonparametric measures of dependence for random variables, Ann. Statist., 9 (1981), 879-885]. Moreover, we provide a possible value for that possible, leaving its proof as an open problem.
کلیدواژه‌ها
‎Copula؛ Schweizer and Wolff's $sigma$‎, ‎Spearman's $rho$‎
مراجع
[1] G. Beliakov, A. Pradera and T. Calvo, Aggregation Functions: A Guide for Practitioners, Studies in Fuzziness and Soft, Springer, Berlin, (2007).
[2] F. Durante and C. Sempi, Principles of Copula Theory, Chapman & Hall/CRC, Boca Raton, (2016).
[3] M. Grabisch, J. L. Marichal, R. Mesiar and E. Pap, Aggregation Functions, Encyclopedia of Mathematics and its Applications, 127, Cambridge University Press, Cambridge, (2009).
[4] P. R. Halmos, Measure Theory, Springer, New York, (1974).
[5] R. B. Nelsen, An Introduction to Copulas, Second Edition. Springer, New York, (2006).
[6] A. Renyi, On measures of dependence, Acta Math. Acad. Sci. Hungar., 10 (1959), 441-451.
[7] M. Scarsini, On measures of concordance, Stochastica, 8 (1984), 201-218.
[8] B. Schweizer and E. F. Wol , On nonparametric measures of dependence for random variables, Ann. Statist., 9 (1981), 879-885.
[9] A. Sklar, Fonctions de repartition a n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8 (1959), 229-231.
[10] C. Spearman, The proof and measurement of association between two things, Am. J. Psychol., 15 (1904), 72-101.
[11] E. F. Wol , Measures of dependence derived from copulas, Ph.D. Thesis, University of Massachussetts, Amherst, USA, (1977).

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