Generalized inference for Weibull distributions.

摘要

In this dissertation, we have provided generalized variable (GV) procedures for making inference for some problems involving Weibull distributions. One-sample as well as two-sample problems are considered. It is shown that the GV approach produces exact inferential procedures for one-sample problems such as setting confidence limits on quantiles and survival probabilities. GV methods are given for making inference on a Weibull mean, for constructing prediction limits and for obtaining upper prediction limits that include at least l of m observations from a Weibull distribution at each of r locations. GV procedures are also given for comparing two Weibull means, comparing scale parameters when the shape parameters are unknown and arbitrary, setting confidence bounds on stress-strength reliability involving two independent Weibull random variables, and estimating the ratio of two survival probabilities. The procedures can be easily extended to the type II censored samples, and they can be used to find approximate inferential procedures for type I censored samples. The proposed GV methods are conceptually simple and easy to use. The GV procedures are illustrated using several practical examples.