Locally optimal tests for exponential distributions with type-I censoring

This article studies a locally optimal test [phi]* for testing H0:[theta]>=[theta]0 versus H1:[theta]<[theta]0 for the lifetime parameter [theta] in an exponential distribution based on type-I censored data. Certain properties associated with [phi]* are addressed. We compare the performance of [phi]* with that of Spurrier and Wei's [Spurrier, J.D., Wei, L.J., 1980. A test of the parameter of the exponential distribution in the type-I censoring case. J. Amer. Statist. Assoc. 75, 405-409] test [phi]SW, which is based on the MLE of [theta]. The exact powers and asymptotic powers of [phi]* and [phi]SW are computed. The numerical results indicate that the power of [phi]* is better than that of [phi]SW when [theta](0<[theta]<[theta]0) is close to [theta]0.