MLE, distribution fittings and model calibrating are for sure fascinating topics. Furthermore, from the outside, they might appear to be rocket science. As far I'm concerned, when I did not know what MLE was and what you actually do when trying to fit data to a distribution, all these tecniques did looked exactly like rocket science.

They are not that much complicated though. MLE is a technique that enables you to estimate the parameters of a certain random variable given only a sample by generating a distribution which makes the observed results the most likely to have occurred. Distribution fittings, as far as I know, is the process of actually calibrating the parameters to fit the distribution to a series of observed data.

Let's see an example of MLE and distribution fittings with Python. You need to have installed scipy, numpy and matplotlib in order to perform this although I believe this is not the only way possible. For some reason that I ignore, the methods in scipy.stats related to the normal distribution use loc to indicate the mean and scale to indicate the standard deviation. I maybe can grasp why use "scale" to indicate the stdv however I really do not get "loc" I do not understand why... If you know that, please leave a comment.

The result should look somewhat like this:

Hope this was useful.

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