Relationships Among Common Univariate Distributions

limits can be used in conjunction with a normalizing transformation, as illustrated by the logarithmic transformation in the preceding example from Nelson (1982). Transformations to achieve approximate normality are especially important in light of the lack of robustness of the prediction limits noted earlier. 2. Some instructors may wish to contrast prediction limits with tolerance limits; the former refers to limits for a single independent observation from a normal population, and the latter refers to limits within which a certain fraction of the entire normal population is claimed to lie. 3. The prediction limits (2.3) can be extended readily to include the case of predicting the mean of m new observations in an independent random sample from the same normal population. In this case the 1 a limits for the predicted mean have the form