How does matlab do maximum likelihood on custom functions?

I am trying to fit a custom function ( generalized Normal distribution type II http://en.wikipedia.org/wiki/Generalized_normal_distribution)to my data and i am using mle function. I wonder what is the method that Matlab uses, is it a search method?

Answer 1

[Peter Perkins]

Ordinarily, the mle function minimizes the negative log-likelihood that you have defined (either as a PDF, or a log PDF, or as the LL) using fminsearch. If you have the Optimization Toolbox, you can tell mle to use fmincon. This is the 'OptimFun' parameter, explained in the help for the mle function.

[sepideh]

Thanks, using mle i find this warning :Warning: Maximum likelihood estimation did not converge. Iteration limit exceeded. How much i can trust the answers and how can i change the number of iterations?

[Peter Perkins]

Not at all if it didn't converge, and

>> help mle
 mle Maximum likelihood estimation.
[snip]
       'options'      A structure created by a call to STATSET, containing
                      numerical options for the fitting algorithm.  Not
                      applicable to all distributions.

Answer 2

[gujax]

Hi,

I would like to explore the above question further...

If I use a standard distribution listed in Matlab document and not my custom, how is mle evaluated? For example if the distribution is Poisson, does mle evaluate minimum of log pdf i.e. does it convert to log pdf? So If i provide a pdf, do I have to state that its a log pdf?

Thanks

[Jeff Miller]

1) Just guessing here, but matlab probably obtains the mle's differently for different distributions, because: for some distributions the mle's are simple functions of the data values, and for other distributions you have to use numerical search.

2) When doing numerical search, matlab probably converts to log pdf to minimize numerical problems.

3) If you provide your own pdf, you definitely would have to provide the pdf or indicate that it is the log pdf (if the mle function has an option for that). The parameters that maximize the product of the pdf values are not necessarily the same as those that maximize the product of the log pdf values.