how do i apply maximum likelihood estimation for a gaussian distribution?

I have written a short code of converting an image into normal distribution as follows;

a=imread('lena.jpg'); A=rgb2gray(a); P1=im2double(A); K = P1(:) PD=fitdist(K,'normal')

Now how do i apply Maximum likelihood on it to get the estimates of mean and std. deviation?

Answer 1

[Brendan Hamm]

Maximum Likelihood estimates for a normal distribution would be:

mu = mean(K);
sigma = std(K,1); % 1 for population standard deviation.

However, when we fit Normal distributions we use the Best Unbiased Estimate, which is:

mu = mean(K);
sigma = std(K); % Sample standard deviation

These values can be found in the PD object you fit:

muFit = PD.mu;
sigFit = PD.sigma;