Confidence Intervals for Comparing Two Life Distributions

The performance of several s-confidence interval procedures for comparing two life distributions is studied by Monte Carlo methods. Three life models are considered: exponentials, nonparametric proportional hazard functions (Lehmann alternatives), and nonparametric scale alternatives. The s-confidence procedures are based on a) for exponential distributions: The F-statistic, a likelihood ratio statistic (LR), and maximum likelihood estimator (MLE), b) for nonparametric proportional hazard functions, a LR and MLE based on Cox´s conditional likelihood function, c) for nonparametric scale alternatives, the generalized Wilcoxon and the Cox-Mantel statistics. The procedures are compared with respect to coverage probabilities, robustness, and power. The simulations include several cases of censored and uncensored samples from the Weibull distribution. When samples are from exponential distributions, with or without censoring, all the procedures are valid. The three parametric procedures have higher power than the nonparametric procedures when there is no censoring and have similar power when there is censoring. When samples are from the Weibull distributions, the three parametric procedures are not robust. If the two shape parameters are equal, the procedures for scale alternative models and for proportional hazard models are valid. If the shape parameters are not equal, none of the procedures are appropriate and some more complicated method should be used.