DISTRIBUTION OF THE SAMPLE CORRELATION COEFFICIENT FOR NONNORMAL POPULATIONS

Let r be the correlation coefficient formed from a sample of size n from a bivariate population with the distribution function F. Assume that F has finite cumulants and product cumulants of total order eight. This paper presents the approximate cumulants of the distribution of r up to the fourth order. The Edgeworth expansion for probability integrals and the Cornish-Fisher inverse expansion for percentiles of order 1/n are also given. A numerical experiment demonstrates the substantial effects in approximation of using the higher order terms.