Publication Date


Series Number

Preprint # 2011-2


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)% 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). This paper identifies the conditions under which the coverage probability for the SCB procedure is exactly (1−α). A small simulation illustrates the important theoretical results in the paper.


This preprint was published as Yili Hong, Luis A. Escobar, William Q. Meeker, "Coverage Probabilities of Simultaneous Confidence Bands and Regions for Log-Location-Scale Distributions", Statistics and Probability Letters (2010): 733-738, doi: 10.1016/j.spl.2010.01.003.