On the distribution of _rin samples from the mixtures of bivariate normal populations

Abstract

The distributions of some transformations of the sample correlation coefficient r are studied here, when the parent population is a mixture of two standard bivariate normals. The behavior of these transformations is assessed through the first four standard moments. It is shown that there is a close relationship between the behavior of the transformed variables and the lack of normality as evinced by the 'kurtosis' defined in the bivariate population

Keywords:

• mixtures of bivariate normals
• correlation coefficient
• multivariate measures of skewness and kurtosis
• transformations of _r
• robustness