Coverage probabilities of simultaneous confidence bands and regions for log-location-scale distributions

A simultaneous confidence band (SCB) for the cumulative distribution function (cdf) of a random variable can be used to assess the statistical uncertainty of the estimated cdf. Cheng and Iles (1983) presented a general approach of constructing an SCB   for the cdf of a continuous random variable derived from a 100(1−α)%100(1−α)% simultaneous confidence region (SCR) for the parameters of the distribution. The Cheng and Iles SCB   procedure includes the true cdf with probability at least (1−α)(1−α). This paper identifies the conditions under which the coverage probability for the SCB   procedure is exactly (1−α)(1−α). A small simulation illustrates the important theoretical results in the paper.