Maximum likelihood estimation for sum of series

Hello,

Im trying to estimate the maximum likelihood for a sum of series. Right now my code looks like this:

a=[30 20 30]
b=[50 10 40]

F = symsum(log(exp(a*k)/(exp(a*k)+exp(b*k))),k,[0 3])


custlogpdf = @(data,k) F 


phat = mle(test.individuum,'logpdf',custlogpdf,...
    'start',[1])

My custom distribution should be this funktion

and P in this case are

How do I insert the funktion into the symsum? I hope someone can help me with this problem.

Answer 1

[Matt J]

The mle command is not a symbolic solver. You must use a regular numeric implementation of your logpdf to apply mle().

a=[30 20 30]
b=[50 10 40]

phat = mle([a;b],'logpdf',@custlogpdf,'start',[1]);

function LL=custlogpdf(data,beta)

  a=data(1,:);
  b=data(2,:);  
  
  LL=sum(1./exp(beta*(b-a)));
  
end

[Marcel]

Hey, thank you for your help.

The mle() doesn't accept [a;b]. I get the error message "Data must be a vector".

[Matt J]

I see. Well, then by all means go ahead and make it a vector instead.