Locally best tests for exponential distributions with interval-censored data

Abstract

In this article, we derive a locally best test for testing the mean of exponential distributions with interval-censored samples. This locally best test possesses certain optimality. It is of unbiasedness and equivalent to a likelihood ratio test in some circumstances, and it is also a Bayes test for some loss function. For the locally best test, the associated critical values and powers at a nominal level of significance are provided. For a large sample size case, asymptotic critical values and powers are also calculated and tabulated. Moreover, based on the locally best test, a curtailed test is proposed. This curtailed test is equivalent to the locally best test on the acceptance or rejection of the null hypothesis. A Monte Carlo simulation is carried out to illustrate the performance of the curtailed test compared with the locally best test. Numerical results show that the experimental duration time of the curtailed test is substantially smaller than that of the locally best test.

Keywords:

• exponential distribution
• interval-censored sample
• likelihood ratio test
• locally best test
• curtailed test

Mathematics Subject Classifications:

• 62F15
• 62C10

Acknowledgement

This research was supported by NSC 101-2118-M-130-001 of the National Science Council in Taiwan.