I am learning about the likelihood ratio test. Is the LRT applicable for non-Gaussian distributions too? Up to now I have only been able to find examples of the LRT for Gaussian and Gaussian mixture models.
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$\begingroup$ why do you think it might not be? Gaussian is simple and nice and almost everyone - in practice - believes everything is Gaussian so "the focus shall be on it" is a fashion/markt-driven issue :-) $\endgroup$– Math-funCommented Jun 28, 2017 at 13:49
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$\begingroup$ @Math-fun Maybe my search isn't efficient but I am not able to find any references or articles which use LRT for such distributions. Any suggestions? $\endgroup$– ShreedharCommented Jun 28, 2017 at 14:12
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$\begingroup$ Take a look at Neyman-Pearson Lemma :-) $\endgroup$– Math-funCommented Jun 28, 2017 at 14:29
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$\begingroup$ I'm curious what you did to search, since typing likelihood ratio test into our search bar turns up as its second hit a question about a non-Gaussian case. Then after that the fourth, sixth and seventh hits (which is as far as I looked) are all non-Gaussian; some of them are answered, too, though their mere existence answers your question). What were you searching for? $\endgroup$– Glen_bCommented Jun 28, 2017 at 23:56
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The Neyman-Pearson lemma is pretty general and is not limited to the Gaussian case. Also see the Wikipedia article on the likelihood ratio test, which simply refers to some $f(x|\theta)$.
Searching our site on likelihood ratio test turns up numerous examples of questions about non-Gaussian cases.
There are also at least four examples in the "Related" section in the sidebar on the right side of this page.
