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Normal-approximation tests for a Poisson exposure model

For testing

H_{0} : θ = 1

against a larger alternative, approximate size-

0.05

upper-tail tests reject when

θ_{M L E} > 1 + \frac{1.645}{S _{1}}

or, respectively,

θ_{L S} > 1 + 1.645 \frac{S _{3}}{S _{2}} .

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