Approximate inference for location and scale parameters with application to failure-time data

A new method (SP/CI) for obtaining approximate confidence intervals for the location, scale, and quantiles based on sample data parameters is presented. The basis of SP/CI is a saddlepoint expansion; the requirements are the maximum likelihood estimate (MLE), a few cross derivatives of the log-likelihood evaluated at the MLE, and quantiles of the log(F) distribution. SP/CI is illustrated numerically on several type-II censored reliability data sets using the extreme value and log-normal models. The accuracy is investigated by numerical comparison with the exact results, with best linear invariant estimator (BLIE), as well as with the results from other approximate methods discussed in the literature, including the asymptotic normality of the MLE, the likelihood ratio (LR) statistic, and corrections to the LR statistic recently developed