Exact Likelihood Inference for k Exponential Populations Under Joint Type-II Censoring

Abstract

In this paper, when a jointly Type-II censored sample arising from k independent exponential populations is available, the conditional MLEs of the k exponential mean parameters are derived. The moment generating functions and the exact densities of these MLEs are obtained using which exact confidence intervals are developed for the parameters. Moreover, approximate confidence intervals based on the asymptotic normality of the MLEs and credible confidence regions from a Bayesian viewpoint are also discussed. An empirical comparison of the exact, approximate, bootstrap, and Bayesian intervals is also made in terms of coverage probabilities. Finally, an example is presented in order to illustrate all the methods of inference developed here.

Keywords:

• Bayesian inference
• Bootstrap intervals
• Confidence bounds and intervals
• Coverage probabilities
• Exponential distribution
• Joint Type-II censoring
• Likelihood inference

Mathematics Subject Classification:

• 62E15
• 62F03
• 62N01, 62N02
• 62N03