Locally optimal tests for exponential distributions with type-I censoring

This article studies a locally optimal test φ for testing H0 : θ ≥ θ0 versus H1 : θ < θ0 for the lifetime parameter θ in an exponential distribution based on type-I censored data. Certain properties associated with φ are addressed. We compare the performance of 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 φSW , which is based on the MLE ∧ θML of θ . The exact powers and asymptotic powers of φ and φSW are computed. The numerical results indicate that the power of φ is better than that of φSW when θ(0 < θ < θ0) is close to θ0. c © 2007 Elsevier B.V. All rights reserved.