A Note on the Comedian for Elliptical Distributions

AbstractThe comedianCOM(X,Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X,Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the correlation coefficientρwith range [−1,1] and can therefore serve as a robust alternative toρ. We show that this result, which is not true in general, extends to elliptical distributions even in the case where moments ofX,Ydo not exist