# Thread: how to calculate AIC criteria where model represent pdf with several parametrs

1. ## how to calculate AIC criteria where model represent pdf with several parametrs

Hello,
by definition AIC is a simple formula for estimating models,
AIC=2k-2ln(L), where L -s maximum log likelihood,
how to calculate AIC when fiitted model represents a PDF with several parameters?
For example If I want to fit data to a normal distribution,
I get 2 values of MLE (for mu and sigma).
Many thanks in advance

2. I could be wrong, but I believe you can use the MSE as an estimate for $\displaystyle \sigma$.

In particular, Kutner, et al., "Applied Linear Statistical Models" (5th ed.) say on page 32 that:

$\displaystyle s^2 = MSE = \frac{n}{n-2}\hat\sigma^2$

3. I'm not sure I understand the issue. Just plug in the MLE's into the likelihood and calculate it. Typically you would use AIC to compare multiple models; if you don't have any alternative models other than the simple normal model then there isn't much else to do.