Locally optimal tests for exponential distributions with type-I censoring

• Published in: Computational statistics & data analysis 2008-03, Vol.52 (7), p.3603-3615
• Main Authors: Liang, Tachen, Huang, Wen-Tao, Yang, Kun-Cheng
• Format: Article
• Language: English
• Subjects: Distribution theory; Exact sciences and technology; General topics; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2007.11.015

This article studies a locally optimal test φ ∗ for testing H 0 : θ ≥ θ 0 versus H 1 : θ < θ 0 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 φ S W , which is based on the MLE θ M L ∧ of θ . The exact powers and asymptotic powers of φ ∗ and φ S W are computed. The numerical results indicate that the power of φ ∗ is better than that of φ S W when θ ( 0 < θ < θ 0 ) is close to θ 0 .