mle with cdf

Question

Peon Pion 2011-10-11

1
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https://ww2.mathworks.cn/matlabcentral/answers/18014-mle-with-cdf

评论： junsoo lee 2016-5-28

Hi

I was wondering if someone can shed light on mle with cdf. It always returns two estimates, regardless of of how many parameters you have. Moreover,the second estimate is the std of the input. e.g. If you run the following:

r = randn(100,1)*20+10;

pdf_norm = @(x,mu) = normpdf(x,mu,20);

cdf_norm = @(x,mu) = normcdf(x,mu,20);

[p1,c1]=mle(r,'pdf',pdf_norm,'start',5);p1

[p2,c2]=mle(r,'cdf',cdf_norm);p2

you see that p2 has two elements, when it should have only 1. What is the correct way of using mle with cdf if you do NOT have a pdf? How do you use mle with cdf if you have to estimate more than one parameter?

Thanks,

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Answer 1

Peter Perkins 2011-10-12

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在 MATLAB Online 中打开

This

[p2,c2]=mle(r,'cdf',cdf_norm);

is not a valid syntax for the MLE function (for two reasons, but I'll assume you left out 'start' by accident). The help is perhaps not clear enough about this, but if you do not specify one of the two dozen or so "canned" distributions, then you MUST pass in either the PDF, or the log PDF, or the negative log-likelihood. The above syntax, without the 'pdf' input, is not ever shown in the help (if it is, please let us know where, it's a documentation bug).

It turns out that because you didn't provide 'pdf', or 'logpdf', or 'nloglf', MLE assumes you must want one of the "canned" distributions, and because you didn't specify one, it assumes 'normal'. You 'cdf' input is ignored.

So, you cannot use MLE if you do not have a PDF -- it does not auto-differentiate the CDF. If you absolutely cannot compute the PDF, you might take a look at the Fitting a Univariate Distribution Using Cumulative Probabilities demo that ships with the Statistics Toolbox.