Approximate Confidence Limits on the Mean of X + Y Where X and Y Are Two Tabled Independent Random Variables

A general method is developed for obtaining confidence limits on the mean of X + Y where X and Y are two independent random variables whose individual distributions and percentiles are in standard statistical tables. The procedure uses this information to obtain approximations for the percentiles of the sum or approximate confidence limits on the mean of the sum. The method is applied to two problems: approximating the percentiles of the noncentral t distribution, and determining confidence limits for variance components in a one-way classification. Numerical examples compare it to other approximations.