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ON THE UNIFORMLY MOST POWERFUL TEST FOR THE LOCATION PARAMETER OF AN EXPONENTIAL DISTRIBUTION
Keywords:
uniformly most powerful test, unbiasedness.DOI:
https://doi.org/10.17654/0972086324009Abstract
For testing the location parameter $\mu$ of the two parameter exponential model, a broad class of uniformly most powerful unbiased tests for the hypothesis of $\mu=0$ verses $\mu<0$ is derived. Examples are also given to show that for testing this model, there is no uniformly most powerful test for the hypothesis of $\mu=0$ verses either $\mu \neq 0$ or $\mu<0$ as claimed in the literature.
Received: December 26, 2023
Accepted: February 24, 2024
References
D. G. Kabe and A. G. Laurent, On some nuisance parameter free uniformly most powerful tests, Biom. J. 25 (1981), 245-250.
E. L. Lehmann, Theory of Point Estimation, Wiley, New York, 1983.
E. L. Lehmann, Testing Statistical Hypotheses, Wiley, New York, 1986.
E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, Springer, New York, 2005.
K. Takeuchi, A note on the test for the location parameter of an exponential distribution, Ann. Math. Statist. 40 (1969), 1838-1839.
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