On testing equality of two exponential distributions under combined type II censoring

The problem of testing equality of the scale parameters of two exponential distributions is considered under a combined sample type II censoring scheme that has been extensively treated in nonparametric inference. Sufficiency and invariance considerations lead to a pair of statistics, namely, the proportions of failure count and the total time on test of the first sample to those of the combined sample. Exact distribution and moment properties are discussed, and asymptotic joint normality under local alternatives is established in a general framework. An invariant test that maximizes the Pitman efficiency is seen to be based on the difference between these two proportions, and it is asymptotically equivalent to the likelihood ratio test.