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Frank’s family of bivariate distributions. (English) Zbl 0635.62038
This paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent. The proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the Fréchet bounds as well as the distribution corresponding to independent variables. Three nonparametric estimators of the association parameter are suggested and Monte Carlo experiments are used to compare their small-sample behaviour to that of the maximum likelihood estimate.

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62G05 Nonparametric estimation
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