Abstract
Recent investigations about notions of bivariate aging have underlined the need to introduce some new properties of positive dependence for a bivariate random vector. Here, by using the recent notion of supermigrativity of a bivariate copula, a positive dependence property is introduced and investigated. Comparisons with other notions of positive dependence are also presented.
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Bassan, B., Spizzichino, F.: Bivariate survival models with Clayton aging functions. Insur. Math. Econ. 37(1), 6–12 (2005a)
Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivar. Anal. 93(2), 313–339 (2005b)
Bustince, H., Montero, J., Mesiar, R.: Migrativity of aggregation functions. Fuzzy Sets Syst. 160(6), 766–777 (2009)
Cuadras, C.M., Augé, J.: A continuous general multivariate distribution and its properties. Commun. Stat., Theory Methods 10(4), 339–353 (1981)
Durante, F.: A new class of symmetric bivariate copulas. J. Nonparametr. Stat. 18(7–8), 499–510 (2006)
Durante, F., Ghiselli-Ricci, R.: Supermigrative semi-copulas and triangular norms. Inf. Sci. 179(15), 2689–2694 (2009)
Durante, F., Sarkoci, P.: A note on the convex combinations of triangular norms. Fuzzy Sets Syst. 159(1), 77–80 (2008)
Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Semilinear copulas. Fuzzy Sets Syst. 159(1), 63–76 (2008)
Durante, F., Foschi, R., Spizzichino, F.: Ageing function and multivariate notions of NBU and IFR. Probab. Eng. Inf. Sci. 24(2), 263–278 (2010)
Fodor, J., Rudas, I.J.: On continuous triangular norms that are migrative. Fuzzy Sets Syst. 158(15), 1692–1697 (2007)
Guan, K.: Some properties of a class of symmetric functions. J. Math. Anal. Appl. 336(1), 70–80 (2007)
Härdle, W., Okhrin, O.: De copulis non est disputandum. Copulae: an overview. AStA Adv. Stat. Anal. 94(1), 1–31 (2010)
Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds.): Copula Theory and Its Applications. Lecture Notes in Statistics—Proceedings, vol. 198. Springer, Berlin (2010)
Kimeldorf, G., Sampson, A.R.: A framework for positive dependence. Ann. Inst. Stat. Math. 41(1), 31–45 (1989)
Lai, C.D., Xie, M.: Stochastic Ageing and Dependence for Reliability. Springer, New York (2006)
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Mathematics in Science and Engineering, vol. 143. Academic Press [Harcourt Brace Jovanovich Publishers], New York (1979)
Mesiar, R., Bustince, H., Fernandez, J.: α-migrativity of semicopulas copulas and quasi-copulas. Inf. Sci. 180(10), 1967–1976 (2010)
Meyer, C.: The Bivariate normal copula. http://adsabs.harvard.edu/abs/2009arXiv0912.2816M (2009)
Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer Series in Statistics. Springer, New York (2006)
Spizzichino, F.: Subjective Probability Models for Lifetimes. Monographs on Statistics and Applied Probability, vol. 91. Chapman & Hall/CRC, Boca Raton (2001)
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Durante, F., Ghiselli-Ricci, R. Supermigrative copulas and positive dependence. AStA Adv Stat Anal 96, 327–342 (2012). https://doi.org/10.1007/s10182-011-0165-2
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DOI: https://doi.org/10.1007/s10182-011-0165-2