Finding the maximum likelihood estimates ?

I need to find the MLE estimates. My code is as below. It seems to give me the correct mean but incorrect variance.

 function obj = kmlepdf(x,y)

     f1 = -1*50*log(2*pi*(y(2)));
     f2 = ((y(2)));
     f3 = ((x-y(1)).^2);
     obj = (f1 + sum(0.5*(f3./f2))); % Normal Function

end

 clear all;

 load data;

 y0 = [0.5 0.5];

 lb = [0 0];
 ub = [10 10];
 % Assign Data to a new variable
 x = data;

 % Calling the Least Square Minimization
 opts=optimset('DerivativeCheck','on','Display','off','TolX',1e-6,'TolFun',1e- 6,'Diagnostics','off','MaxIter',200);
 [y, fval] = fmincon(@(y)kmlepdf(x,y),y0,[],[],[],[],lb,ub,[],opts)

Answer 1

[Tom Lane]

I believe you want

f1 = 0.5*length(x)*log(2*pi*(y(2)));

You start with 1/sqrt(2*pi*sigma^2), then take logs so you get a minus sign, but you need to negate again to get the negative log likelihood that you can minimize.

Also try setting lb(2)=eps.