COMPARISONS OF APPROXIMATE CONFIDENCE-INTERVALS FOR DISTRIBUTIONS USED IN LIFE-DATA ANALYSIS

This article evaluates the accuracy of approximate confidence interval s for parameters and quantiles of the smallest extreme value and norma l distributions. The findings also apply to the Weibull and the lognor mal distributions. The interval estimates are based on (a) the asympto tic normality of the maximum likelihood estimator, (b) the asymptotic chi2 distribution of the likelihood ratio (LR) statistic, (c) a mean a nd variance correction to the signed square roots of the LR statistic, and (d) the Bartlett correction to the LR statistic. The extensive Mo nte Carlo results about true error probabilities and average lengths u nder various degrees of censoring show advantages of the LR-based inte rvals. For complete or moderately censored samples, the mean and varia nce correction to the LR statistic gives nearly exact and symmetric er ror probabilities. In small samples with heavy censoring, the Bartlett correction tends to give conservative error probabilities, whereas th e uncorrected LR interval is often anticonservative. The results also indicate that LR-based methods have longer interval lengths than inter vals based on the asymptotic normality of the maximum likelihood estim ator.