Computer algebra application to the distribution of sample correlation coefficient Original Research Article

Let r be the sample correlation coefficient. In this paper, we clarify the role of computer algebra to obtain an asymptotic expansion for probability integrals of r. A key technique is to use a change of bases of the module of symmetric polynomials. We describe an algorithm for accomplishing it. We derive the asymptotic cumulants of r in terms of population cumulants. An approximate distribution of r is also given.