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Biometrika 1987 74(3):549-555; doi:10.1093/biomet/74.3.549
© 1987 by Biometrika Trust
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Frank's family of bivariate distributions

CHRISTIAN GENEST

Department of Statistics and Actuarial Science, University of Waterloo Waterloo, Ontario, Canada N2L 3G1

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.

Key Words: Association parameter • Bivariate distribution • Copula • Nonparametric estimation • Plackett's family • Rank correlation • Total positivity


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