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May 17, 2018 at 12:35 comment added Nick Cox In principle any probability or probability density being 0 means that the likelihood is 0 and the log-likelihood is indeterminate. In principle also saying that the likelihood is zero amounts to saying that some observed data are impossible and that surely means a misspecified model. So in practice only positive values for $f$ enter your equation.
May 17, 2018 at 12:31 history edited Nick Cox CC BY-SA 4.0
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May 17, 2018 at 12:14 history edited Tim CC BY-SA 4.0
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May 17, 2018 at 10:29 vote accept Maryam
May 17, 2018 at 10:29 comment added Tim @Maryam this should be explained in any mathematical statistics handbook, since follows from the definitions.
May 17, 2018 at 10:26 comment added Maryam Thank you so much for your great answer. I am working on a project and I would like to clearly understand it. Could you advise me on some peer-review paper or a book about this, please? this will be very helpful to discuss it with my supervisor.
May 17, 2018 at 10:21 history answered Tim CC BY-SA 4.0