Talk:Neyman-Pearson lemma

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Can someone add a more detailed explaination and an example to this article?

The symbol used for the ratio is the symbol used in the likelihood ratio test article, even though the likelihoods there are the maximum likelihoods. I suppose seeing as there is only one possible value under each hypothesis that specifying they are the supremums is not strictly necessary but it might be technichally correct.

Also the likelihood ratio test article says that the null hypothesis has to be a subset of the alternative hypothesis whereas here that is not the case. Possibly this is a generalised likelihood ratio test as described here: http://www.cbr.washington.edu/papers/zabel/chp3.doc7.html where there are only two possible values of the parameter theta?