Negative binomail distribution and its variance

[_joey]

Hi,

I am trying to estimate variance for negative Binomial distribution using
maximum likelihood estimation and Expected (Fisher's) information to determine its variance. I know what variance is for this distrubution but I cannot derive it.


Here is my solution. Any comments and suggestions are much appreciated

Thanks!

Solution: http://img825.imageshack.us/img825/7545/ndist.png

 

[_joey]

I think I know what the problem is. I've been solving problems for many hours and I need a break. :)

 

[QuendeltonPG]

Have you tried putting it into the form of the exponential family first?

Your MLE = x bar is incorrect. What did you get for your log-likelihood function?