Abstract
Summary Let Tr (r = 0, 1, …) be independent, positive, exponentially distributed random variables with parameters λ + rΨ. It is shown that the uniformly most powerful unbiased test of the null hypothesis Ψ = 0 against alternatives Ψ > 0 rejects the former for small values of Z=(∑r=1nrTr)(∑r=0nTr)−1. The power function of the test is given and the test is shown to be consistent. Unbiasedness is shown for a wider class of alternatives. A sequential version of the test is presented. A generalization of the results for a model relevant to accident research is given in the last section of the paper. Selected values of the power function are tabulated in the Appendix.
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