Robustness to nonnormality of some transformations of the sample correlation coefficient

In this paper, some of the familiar transformations of r are examined for their robustness to nonnormality. General results are given for any parent population f(x, y) and any general transformation g(r) of r. Two types of parent populations are considered for exemplification: The bivariate Edgeworth series distribution and the truncated bivariate normal distribution. The effects of nonnormality are assessed through the parameters [mu]'1, [mu]2, [gamma]1, [gamma]2. Tables are provided comparing these quantities against their bivariate normal counterparts.