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Properties of a one-parameter family of bivariate distributions with specified marginals. (English) Zbl 0616.62067
Using a family of functions first described by M. J. Frank [Aequationes Math. 19, 194-226 (1979; Zbl 0444.39003)], a one-parameter family of bivariate distributions is constructed. This family has arbitrary marginals and contains the Fréchet bounds as well as the member corresponding to independent random variables. Three nonparametric measures of correlation (Spearman’s rho, Kendall’s tau, and the medial correlation coefficient) are evaluated, and a simple transformation to generate random samples from an arbitrary member of the family is presented.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
60E05 Probability distributions: general theory
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