Factors for Calculating Two-Sided Prediction Intervals for Samples from a Normal Distribution

Abstract

Factors r(k, n; γ) for a normal distribution are given such that one may be 100γ% confident that the two-sided prediction interval will contain all of k future values, where and s are the sample mean and standard deviation from n previous observations. A special case is a prediction interval for a single future observation, which can also be obtained using percentage points of the Student t-distribution. Curves which indicate the extent to which two previously proposed approximations over-estimate r(k, n; γ) are also given. One of these, based on a Bonferroni Inequality, gives generally satisfactory results for all cases except for small n and large k, but frequently requires unusual percentage points of the Student t-distribution.