Exact likelihood inference for two exponential populations under joint Type-II censoring

Comparative lifetime experiments are of paramount importance when the object of a study is to ascertain the relative merits of two competing products in regard to the duration of their service life. In this paper, we discuss exact inference for two exponential populations when Type-II censoring is implemented on the two samples in a combined manner. We obtain the conditional maximum likelihood estimators (MLEs) of the two exponential mean parameters. We then derive the moment generating functions and the exact distributions of these MLEs along with exact confidence intervals and simultaneous confidence regions. Moreover, simultaneous approximate confidence regions based on the asymptotic normality of the MLEs and simultaneous credible confidence regions from a Bayesian viewpoint are also discussed. A 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 discussed here.