Standard Confidence Limits for Linear Functions of the Normal Mean and Variance
Abstract Tables of standard confidence limits for linear functions of the mean and variance of a normal distribution are presented. Algorithms are presented by which confidence limits for an arbitrary linear function μ + λσ 2 can be obtained using the tables given observed values of Y distributed as N(μ,σ 2 /γ 2) and S 2 distributed independently as σ2/v times χ2 with v degrees of freedom, where μ and σ2 are unknown parameters and v, γ, and λ are known but arbitrary numbers.