Series Representation of Non Null Distribution of the Square of Sample Multiple Correlation Coefficient by Use of the Mellin Integral Transform

摘要

The Mellin integral transform is a widely used natural analytical tool that is applied to obtain the distributions of products and quotients of independent random variables. In this article, analytical derivations of the non null density and the cumulative distribution function of the square of sample multiple correlation coefficient are given by use of the Mellin integral transform. The procedure of derivation results in series form representation of the distribution function of the square of sample multiple correlation coefficient.