Exact likelihood-ratio tests for joint type-II censored exponential data

Several results based on the likelihood-ratio test have been discussed in the literature for testing the scale parameters of two exponential distributions under complete and different censored forms of data, many of which are asymptotic in nature. However, exact likelihood-ratio tests have been derived only for the case of complete and independent Type-II censored samples. In this paper, we first develop exact inference using the likelihood-ratio test based on two exponential samples under joint Type-II censoring. We then obtain the exact critical value as well as the power function by using both unrestricted and restricted maximum likelihood estimators (MLEs) in the likelihood-ratio test statistics. Based on these results, we discuss the procedure for designing an optimal life-testing experiment in this set-up. Finally, some numerical examples are presented for illustrating all the results developed here.