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I am studying maximum likelihood estimators (MLE) right now. I am trying to do a little article about how to apply maximum likelihood estimators to one real life problem.

But I see that MLE mostly is about to "prove" estimators to known distributions.

In some universities exams I see that professors give you a probability density function that is very... mmm..."exotic", and you figure out its parameters by MLE, but I'm not sure that those PDFs work in real life.

Am I wrong in my apprehension?

Are there some real applications of MLE in real life for me to write my article about?

kjetil b halvorsen
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Locker05
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    MLE is a big deal for fitting parameters to data, but you always have to choose _some_ form for your model. Maybe it's what your professor gives you. Maybe it's a neural network with (not kidding) billions of parameters, for something like translating text. The general principle of MLE is the same for both. – Arya McCarthy Apr 20 '21 at 02:43
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    As Arya said, MLEs are heavily used in many applications that involve statistics, including, notably, machine learning. If you're looking for a good textbook specifically on likelihoods and MLEs, I suggest *In All Likelihood: Statistical Modelling and Inference Using Likelihood* by Yudi Pawitan. – The Pointer Apr 20 '21 at 02:49
  • thank you Arya. I didn't know it was applied in neuronal netwoek as well.. thank you @The pointer , I really wanted a book like that. Thank you. – Locker05 Apr 20 '21 at 04:34
  • and , for example I have a histogram. .how can I make my own PDF from it ? are there some tecnic ? – Locker05 Apr 20 '21 at 06:34
  • You could find some help here: https://stats.stackexchange.com/questions/112451/maximum-likelihood-estimation-mle-in-layman-terms/112480#112480 – kjetil b halvorsen Apr 20 '21 at 17:56

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