Practical Small-Sample Asymptotics for Distributions Used in Life-Data Analysis

Fraser (1968) and Lawless (1982, Appendix G) discussed exact conditional intervals for the parameters and quantiles of the location-scale model when complete data are used. Moreover, Lawless (1982) extended the exact method to failure-censored (Type II censored) data. Nevertheless, the exact intervals are diicult to obtain in practice and are unavailable under time censoring (Type I censoring). As a consequence, approximate large-sample intervals are widely used. In this article, a likelihood based third order procedure is developed. The method does not require explicit nuisance parameterization and can be easily implemented into algebraic computational packages. Numerical examples are presented to show the accuracy of the method even when the sample size is small.