## CRLB mistake (Gamma)

Hi, Thank you for looking. (Please allow Theta to be represented by G)

I have a random sample from GAM(G,2), where G is unknown. I need to find the CRLB for the variances of the unbiased estimators of G.

I am using the CRLB formula which requires the Expected value of the second derivative of the log of the pdf function.

I have, as my first derivative of the log of the pdf : -G^(-2) + xG^(-2)

Therefore the second derivative is: -2G^(-3) - 2xG^(-3),
which equals: (2-2x)/(G^3)

So the expected value of the second derivative is: [2/G^3] - [(2/G^3)*E(X)]

For Gamma, E(X) = kG, where our k=2, so 2G.

So my expected value for the second derivative is (2-4G)/(G^3)

So using the CRLB formula, I have: 1/{-n(2-4G)/(G^3)},

this gives: 1/{(-2n + 4Gn)/G^3}

= (G^3)/(4Gn - 2n)

= (G^3)/{2n(2G-1)}

I know this is wrong, it should become: g^2/(2n).