How to calculate maximum likelihood estimators of a normal distribution?

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How to calculate maximum likelihood estimators of a normal distribution?



Although there are in principle many examples here on stack overflow (see: Maximum Likelihood Estimate pseudocode) they all differ for what I need or in an other language.
I have data x:


x = pd.Series(np.random.randint(9, high=18, size=255))



Where I calculate the logreturns:


pct_change = x.pct_change()
log_return = np.log(1 + pct_change)
logreturns = log_return.dropna(how='any')



I'm assuming that the logreturns are normally distributed(μ,σ2). How do I calculate the maximum likelihood estimators for μ en σ2 and how do I interpret the results?









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