Parametric Simultaneous Confidence Bands for Cumulative Distributions From Censored Data
This article describes existing methods and develops new methods for constructing simultaneous confidence bands for a cumulative distribution function. Our results are built on extensions of previous work by Cheng and Iles for two-sided and one-sided bands, respectively. Cheng and Iles used Wald statistics with (expected) Fisher information. We consider three alternatives—Wald statistics with observed Fisher information, Wald statistics with local information, and likelihood ratio statistics. We compare standard large-sample approximate methods with simulation or bootstrap-calibrated versions of the same methods. For (log-)location-scale distributions with complete or failure (Type II) censoring, the bootstrap methods have the correct coverage probability. A simulation for the Weibull distribution and time-censored (Type I) data shows that bootstrap methods provide coverage probabilities that are closer to nominal than those based on the usual large-sample approximations. We illustrate the methods with examples from product-life analysis and nondestructive evaluation probability of detection.
This preprint was published in Technometrics 43 (2001): 450–461, doi:10.1198/00401700152672546.