AN APPROXIMATION TO THE DISTRIBUTION OF THE PRODUCT OF TWO DEPENDENT CORRELATION COEFFICIENTS

摘要

Many methodological studies depend on the product of two dependent correlation coefficients. However, the behavior of the distribution of the product of two dependent correlation coefficients is not well known. The distribution of sets of correlation coefficients has been well studied, but not the distribution of the product of two dependent correlation coefficients. The present study derives an approximation to the distribution of the product of two dependent correlation coefficients with a closed form, resulting in a Pearson Type I distribution. A simulation study is also conducted to assess the accuracy of the approximation.