Abstract The article comments on the paper "Extending the Applicability of Probabilistic Management Planning and Control Models," by Stephen L. Buzby, which was published in the January 1974 issue of the journal "The Accounting Review." According to the authors, the use of Tchebycheff inequalities has been made obsolete by improvements in statistical techniques. Second, the tests that result from the use of Tchebycheff inequalities are extremely conservative, because they provide excessive protection against type I errors and, consequently, poorer protection against type II errors. Third, Buzby has made several statements relating to the distribution of products of variables which are contradictory to the nature of those distributions as reported in the statistics literature. Buzby states that the distribution of the product of a number of normally and identically distributed random variables is unknown except in the case where each has a mean of zero and where there is equality of variances. In that case, Buzby claims that the product will possess a chi-square distribution. However, this is in error. In the authors' opinion, it is important to keep in mind that the Tchebycheff inequalities are rather loose and inaccurate in calculating probabilities and that they should mostly be used in theoretical proofs.
Hayya et al. (Wed,) studied this question.