Two-Sided Prediction Intervals to Contain at Least k Out of m Future Observations From a Normal Distribution

Abstract

Prediction intervals are frequently used when it is necessary to use past data to make a statistical statement about a small number of future observations. Given the sample mean and the sample standard deviation s. computed from a random sample of size n from a normal distribution, this article provides factors r = r(k, m, n; γ) such that the two-sided prediction interval ± rs will contain at least k out of m future observations with (1ooγ)% confidence. The original n observations and the additional m observations are assumed to be independent samples from the same normal population. Values of r are given for γ = .90, .95, .99; n = 8(1)12, 1.5, 20, 25, 30, 40, 60, 120, 240, 480, X m = l(l)9 for k = m; m = 10, 15, 20(10)60, 80, 100, for k = m – j, where j = 0(l)8.

KEY WORDS:

• Beta-expectation tolerance intervals
• Multivariate t distribution
• Tables