MLE and Gamma Distribution for econometrics class

#1
Here's an upload of the question, we haven't really covered this material in class


a) My log-like = -a*n ln (b+xi) - n*ln Γ(a) + n*(a-1) ln yi - (yi/(b+xi))

I can get dl/db, but not dl/da

b) I get the solution b=-xi, but that doesn't seem right. I cannot get a solution for a.

My algebra's a little rusty, can you transform SUM(b+xi) into n(b+xi)?

Thanks
 

BGM

TS Contributor
#2
If you have \( n \) sample \( X_1, X_2, ..., X_n \), then the likelihood is the joint pdf but not only the marginal pdf for \( X_i \)

There is no closed form solution for the MLE of \( \alpha \)