Tests for Comparing Several Two-Parameter Exponential Distributions Based on Uncensored/Censored Samples

The problems of comparing several exponential distributions based on type II censored samples are considered. Likelihood ratio tests (LRTs) for comparing several location parameters, comparing several scale parameters and for homogeneity of distributions are derived. The LRTs for all three problems are exact as their null distributions do not depend on any unknown parameters. Algorithms are provided to estimate the exact p-values or the percentiles of null distributions. Approximations to the null distributions that are accurate even for small sample sizes are provided. For testing the equality of scale parameters, the proposed LRT is compared with the tests based on union-intersection method and an iterative procedure. Comparison studies indicate that the LRT is more powerful than the existing ones for most parameter values. The methods are illustrated using an example involving elapsed times from randomization to diagnosis of a serious infection of chronic granulomatous disease that were collected from three different hospitals.