= Shape-two Weibull scale likelihood-ratio test
{c}
{title2=$\sum_iX_i^2\geq(\lambda_0^2/2)q_{2n,1-\alpha}$}
For independent <Weibull distribution> observations of known shape two, the likelihood ratio between any scale $\lambda_1>\lambda_0$ and the null scale $\lambda_0$ increases with $\sum_iX_i^2$. Under the null, $2\sum_iX_i^2/\lambda_0^2$ has a chi-squared distribution with $2n$ degrees of freedom. The same upper-tail critical region is therefore most powerful for every larger scale, giving a uniformly most powerful size-$\alpha$ test.
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