Abstract
A copula is a function of two variables which couples a bivariate distribution function to its marginal distribution functions. In doing so the copula captures certain nonparametric aspects of the relationship between the variates, from which it follows that measures of association and positive dependence concepts are properties of the copula. In this paper we survey results relating copulas to Spearman’s rho and Kendall’s tau for a variety of bivariate distributions, and we also show that certain positive dependence concepts (positive quadrant dependent, right tail increasing, left tail decreasing, and stochastically increasing) can be interpreted as simple geometric properties of the copula.
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Nelsen, R.B. (1991). Copulas and Association. In: Dall’Aglio, G., Kotz, S., Salinetti, G. (eds) Advances in Probability Distributions with Given Marginals. Mathematics and Its Applications, vol 67. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3466-8_3
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DOI: https://doi.org/10.1007/978-94-011-3466-8_3
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