In a recent study of the distribution of Vb1 in sampling from Pearson Type I distributions (Bowman & Shenton, 1973), it was decided to approximate the distribution by equating the lower-order moments to those of some well-known distributions, such as the Pearson system, Gram-Charlier distribution, etc. Since Gram-Charlier and Edgeworth series are apt to produce negative densities in the tails, especially if we include many higher-order terms, say as far as those usually referred to as of order n3, we decided to try the fiveparameter normal mixture