The limit distribution of a random variable used in the construction of confidence bands

Abstract

SUMMARY The limiting distribution of the random variable, √ n times the maximum absolute difference between Φ( x ; x , s ) and Φ( x ;0, 1) is obtained, where Φ( x ;μ,σ) denotes the normal cumulative distribution with mean μ and variance σ 2 and x and s 2 are, respectively, the mean and variance of a random sample of size n from Φ( x ;0, 1).