Probability of sign coincidence centered with respect to sample mean random variables

Probability of sign coincidence of centered random variables is one possible measure of connection. In [4] it was shown that the measure does not depend from generating function in the class of elliptically contoured distributions. This result was obtained for known shift parameter. In the present paper it is proved that for any sample size the probability of sign coincidence centered with respect to the sample mean random variables does not depend on generating function too. Moreover it is proved that the probability of sign coincidence centered with respect to the sample mean random variables is equal to the probability of sign coincidence centered with respect to the shift parameter random variables.