On the covariance between functions

Authors:
C. M. Cuadras
Affiliations:
University of Barcelona, Barcelona, Spain
Venue:
Journal of Multivariate Analysis
Year:
2002

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Abstract

The covariance between the functions of two random variables is obtained in terms of the cumulative distribution function. This result generalizes previous formulae given by W. Hoeffding (1940, Schriften Math. Inst. Univ. Berlin 5, 181-233) and K. V. Mardia (1967, Biometrika 54, 235-249). An expansion for the covariance, an inequality, a maximum correlation and other consequences are obtained from this generalization.