# Math Help - unbiased est for gamma

1. ## unbiased est for gamma

X1,...Xn ~ Gamma(lambda,theta)
lambda = shape parameter
theta = scale parameter

we assume that a<lambda*n

I need to prove that:

T=[(gf(n*lambda))/(gf(n*lambda-a))]*[sum(xi)]^-a

is an unbiased estimator of the function T(theta) = theta^a

I have no clue how to start it, any clue will be appreciated. I can type it again as a picture if you fail to understand the question.

thanks

2. what is gf?
what does * mean?
sum xi?

gf means gamma function ( I forgot to mention it )
* is the regular use, multiplication
sum(Xi) = a sum ( sigma ) of the random variables Xi

( picture attached )

4. You need to learn TeX or explain what your newly invented terms mean.

First of all $W=\sum_{i=1}^n X_i \sim\Gamma (n\lambda ,\theta )$.

Next, obtain $E(W^{-a})$ by manipulating the constants.

You never need to integrate these type of moments.

5. thanks for your help, it's appreciated !
sorry for not explaining the terms, I forgot

can you be a bit more specific about "manipulating the constants" ? what do you mean by that, what should I do ?

6. $E(W^{-a})=\int_0^{\infty} w^{-a}f(w)dw$ ....
continue... and incorporate the $w^{-a}$ with the other power of w in the integrand.