Let X1, . . . , Xn be a simple random sample from the distribution with cumulative distribution function (CDF) F , and let
Y1, . . . , Ym be a future, independent simple random sample from the same distribution. We often wish to use the values
from the initial sample to make predictions about the future sample. For example, we might want to predict the maximum,
mean, or median for the future sample. For two general discussions of prediction intervals and other statistical intervals, see
Hahn and Meeker (1991) and Vardeman (1992).