Given a random sample of size n from a Gamma Sigma2 alphaBet

Given a random sample of size n from a Gamma( Sigma^2= alphaBeta^2. alpha. Find the maximum likelihood estimator for the population variance, denoted by alpha, beta) population with known parameter

Solution

MLE is obtained by taking derivative of likelihood function of Gamma(alpha,beta)

Refer this link for more details :

http://www2.econ.iastate.edu/classes/econ671/hallam/documents/Basic_stat_000.pdf