Additional Factors for Calculating Prediction Intervals for Samples from a Normal Distribution

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Abstract
A prediction interval on k future observations is an interval which is said to contain the values of all k such observations with a specified probability based on the results of a past sample of n observations from the same population. Such an interval is frequently required in practical applications. This article provides factors for a normal distribution for These factors were obtained using a new computer program whose accuracy was checked by comparison with existing tabulations. Some results are also given to indicate the extent to which a previously proposed approximation based on a Bonferroni Inequality overestimates the factors for calculating a one-sided prediction limit. Calculating a two-sided 100γ percent prediction interval for γ = 0.90 and many values of k ≤ 20 and n ≥ 4. γ = 0.95 and 0.99 for many values of k ≥ 20 and n = 4 and 5. (Factors for n > 5 were previously given in [9].) Calculating a one-sided 100γ percent prediction limit for γ=0.90, 0.95 and 0.99 for many values of k ≤ 20 and n ≥ 4.

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