# When is the inverse of the Fisher Information exact? (MLE)

I just have a quick question about MLE.

Sometimes, when doing MLE problems, I see that the variance expression gotten from the inverse of the Fisher Information is exactly like what it should be and sometimes it isn't. Is there a reason that for some distributions this method is exact? Also, why is it that for some distributions, for example like $geom0(\pi)$, is it difficult to find an exact formula for $var(\tilde\pi)$?

Thanks so much for your help!

EDIT:

$Geom0(\pi)$ is the geometric distribution where the PMF is $(1-\pi)^y\pi$ where $y=0,1,2,...\infty$ as opposed to $Geom1(\pi)$ where the PMF is $(1-\pi)^{(y-1)}\pi$ where $y=1,2,...\infty$. Sorry for the confusion!

• What does $geom0$ mean? – Glen_b -Reinstate Monica Feb 24 '14 at 4:56
• I have updated the question and hope that clarifies the difference! – nicefella Feb 24 '14 at 17:06
• My apologies. Things should be correct now! – nicefella Feb 25 '14 at 2:41