Some useful integrals and their applications in correlation analysis

The distribution of the product moment correlation coefficient based on the bivariate normal distribution is well known. Recently in many business and economic data, fat tailed distributions especially some elliptical distributions have been considered as parent populations. The normal and t-distributions are well known special cases of elliptical distribution. In this paper we derive some theorems involving double integrals and apply them to derive the probability distribution of the correlation coefficient for some elliptical populations. The general nature of the theorems indicates their potential use in probability distribution theory.