On the covariance between functions

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. © 2001 Elsevier Science (USA).