fitdist - How does it work?

As far as I know, there are two ways to fit the data to a distribution:

1. Using the moments.

2. Maximum likelihood estimation.

Would you please help me understand which method does Matlab uses? How does the 'fitdist' function is used to fit the data into a given distribution?

Thanks in advance.

Berk

Answer 1

[Tom Lane]

The fitdist function uses maximum likelihood. The exceptions are the normal and lognormal distributions. For the normal distribution, the mle of sigma^2 is 1/n times the sum of squared deviations from the mean. But using the factor 1/(n-1) instead is very common, because it makes the variance estimate unbiased. That's what fitdist uses. It does the analogous thing for lognormal.

The mle function uses maximum likelihood even in those two cases.