Abstract: First,we get the exact distribution function of   when the density of  is
a product of r(x; , I) and a polynomial, where r(x; , I) is density function of a mul-
tivariate normal distribution with mean and covariance matrix I. Next, we give the
higher approximation distribution of empirical CR statistics by using the first result.

Key words: Empirical CR Statistics, Edgeworth Expansion, Higher Approximation Dis- tribution