Further results on simultaneous confidence intervals for the normal distribution

Abstract

Based on a random sample from the normal cumulative distribution function ϕ(x; μ, σ) with unknown parameters μ and σ, one-sided confidence contours for ϕ(x; μ, σ), −∞<x<∞, and simultaneous confidence intervals for ϕ(y; μ, σ)−ϕ(x; μ, σ), −∞<x<y<∞, are constructed using the method outlined in [3]. Small sample and asymptotic distributions of the relevant statistics are provided so that the construction could be completely carried out in any practical situation.