How to perform the maximum like ratio test?

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artu' breuer
artu' breuer 2015-10-19
Hi,
I have to test if my data have a gaussian or a double gaussian behaviour with the MAXIMUM LIKELIHOOD RATIO TEST. I have a problem defining a double gaussian and use it as a pdf. The data are composed by an histogram. I normalized it so that the integral is <=1 Below a possible code:
>> data_norm = normrnd(0,1,1000,1);
>> data = hist(data_norm,14);
>> x = 1:14;
>> figure;
>> plot(x,data);
>> data = data/sum(data); % normalize to unit length. Sum of h now will be 1.
>> figure;
>> plot(x,data)
>> Gauss_mle = mle(data);
>> Double_gauss_pdf=@(sigma1,mu1,sigma2,mu2) ((1/sqrt(2*pi*sigma1^2)*exp((x-mu1).^2/(2*sigma1^2))+1/sqrt(2*pi*sigma2^2)*exp((x-mu2).^2/(2*sigma2^2))));
>> Double_gauss_mle = mle(data,'pdf',Double_gauss_pdf,'start',[0;1;0;1]);
When I compute Double_gauss_mle it gives me:
Error using mlecustom (line 166)
Error evaluating the user-supplied pdf function '@(sigma1,mu1,sigma2,mu2)((1/sqrt(2*pi*sigma1^2)*exp((x-mu1).^2/(2*sigma1^2))+1/sqrt(2*pi*sigma2^2)*exp((x-mu2).^2/(2*sigma2^2))))'.
Error in mle (line 229) phat = mlecustom(data,varargin{:});
Caused by:
Error using @(sigma1,mu1,sigma2,mu2)((1/sqrt(2*pi*sigma1^2)*exp((x-mu1).^2/(2*sigma1^2))+1/sqrt(2*pi*sigma2^2)*exp((x-mu2).^2/(2*sigma2^2))))
Too many input arguments.
I also do not know exactly how to proceed once I have the maximum likelihood estimate.
Thank you in advance.

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