Locally optimal tests for exponential distributions with type-I censoring

This article studies a locally optimal test φ∗φ∗ for testing H0:θ≥θ0H0:θ≥θ0 versus H1:θ<θ0H1:θ<θ0 for the lifetime parameter θθ in an exponential distribution based on type-I censored data. Certain properties associated with φ∗φ∗ are addressed. We compare the performance of φ∗φ∗ 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 φSWφSW, which is based on the MLE θML∧ of θθ. The exact powers and asymptotic powers of φ∗φ∗ and φSWφSW are computed. The numerical results indicate that the power of φ∗φ∗ is better than that of φSWφSW when θ(0<θ<θ0)θ(0<θ<θ0) is close to θ0θ0.