Performance of likelihood- based interval estimates for two- parameter exponential samples subject to type i censoring

Inferences on the parameters in a two-parameter exponential lifetime model when the data are Type I censored are limited to asymptotic approximations or to conditional constructions around the observed number of lifetimes. The asymptotic methods are simple to implement when constructing confidence regions on the scale and guarantee time parameters of the model. Their small sample properties have not been previously explored, however. This study provides Monte Carlo results to evaluate these properties. For univariate inference on the scale parameter, convergence of the coverage probabilities to nominal levels is slow until the sample size reaches 25. For the guarantee time parameter, two asymptotically equivalent procedures behave similarly, an F-distribution-based method performing slightly better for smaller sample sizes. In addition, a simultaneous confidence region and confidence bands on the survivor function are constructed from the univariate intervals. Their performance mimics that of the single intervals on the scale parameter, suggesting caution in application when the sample size is small.