ABSTRACT
Thus the random variables corresponding to the size and the shape factors are independently normally distributed with the means and variances just given. If the covariance matrix has this special form, the discriminant analysis can be performed with the help of two factors only. If S does not have this special form, it can sometimes be approximated to this form by first standardizing the variates to have unit variance for each component Xi and then replacing the correlation ?ij between the components Xi, Xj of X by ?, the average correlation among all pairs (i, j). No doubt the discriminant analysis carried out in this fashion is not as efficient as with the true covariance matrix but it is certainly economical.
