# As a part of my work I need the Maximum Likelihood Estimate that maximizes the log-likelihood of a vector. Can I use the in-built function 'mle' for this purpose?

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BIPIN SAMUEL on 25 Aug 2022
Commented: Torsten on 6 Sep 2022
In my work I have a vector of particular length 'L'. I want to maximize the log-likelihood estimate of the vector using maximum likelihood estimation. I have followed the following procedure:
x=[vector(1:L)];
[phat,pci]=mle(x);
des_signal=normpdf(x,phat(1),phat(2));
figure();
plot(des_signal)
However, I donot know whether the above command maximizes the log-likelihood. Also, the output I got was not the exact output that I needed but is somewhat similar. The distribution is assumed to be Normal distribution. Is there any other way to do the problem?
Torsten on 2 Sep 2022
Edited: Torsten on 2 Sep 2022
However, I donot know whether the above command maximizes the log-likelihood.
phat is such that it maximizes the log-likelihood.
Also, the output I got was not the exact output that I needed but is somewhat similar.
Is there any other way to do the problem?
Why ? What is insufficient with what you get from "mle" ?

Shreyas on 2 Sep 2022
Edited: Shreyas on 2 Sep 2022
The ‘mle’ command does not return maximum log-likelihood estimates. Log of the likelihood is used for convenience as it simplifies the calculation for many of the derivations.
log likelihood can be generated by taking log of the output after applying the ‘normpdf’ function.
Example,
>> des_signal = log(normpdf(x, phat(1), phat(2)));
The following functions can be used to get the sum of negative of log likelihood: -
Example,
>> pd = fitdist(x, >Normal>);
>> nll = negloglik(pd);
Regarding the second part of the question, in the code the function ‘normpdf’ evaluates the specified array of scalar values. For generating the normal curve, the input values must be sorted.
Example,
>> x = sort(x);
>> des_signal = normpdf(x, phat(1), phat(2));
Torsten on 6 Sep 2022
No. You have the parameters of the distribution (mu and sigma) using the "fitdist" command. Knowing these values, you can plot the distribution. The maximum likelihood value cannot be sufficient to fix the distribution.

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