# 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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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?

##### 1 Comment

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.

I already asked you to explain what you need.

Is there any other way to do the problem?

Why ? What is insufficient with what you get from "mle" ?

### Answers (1)

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.

Please go through the following links for more information: -

- probability - Theoretical motivation for using log-likelihood vs likelihood - Cross Validated (stackexchange.com) (https://stats.stackexchange.com/questions/289190/theoretical-motivation-for-using-log-likelihood-vs-likelihood)
- Log-likelihood (statlect.com) (https://www.statlect.com/glossary/log-likelihood)

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: -

- fitdist (https://www.mathworks.com/help/stats/fitdist.html)
- negloglik (https://www.mathworks.com/help/stats/prob.normaldistribution.negloglik.html)

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));

##### 4 Comments

Torsten
on 6 Sep 2022

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