Abstract
Suppose (X1, X2, … , Xm) and (Y1, Y2, … , Yn) are independent random samples taken from two gamma populations Gamma (α, β1) and Gamma (α, β1) respectively. Here, α is the common shape parameter and β1, β2 are the rate parameters. We consider the estimation of α when β1 and β2 are unknown. The exact solution for MLE does not exist. Using some numerical method we compute the MLE for each of the parameters. Asymptotic confidence interval for the common shape parameter ‘α’ has been obtained using the information matrix. Further approximate Bayes estimators have been obtained by using two different approximations. A detailed simulation study has been done to numerically compare the bias, mean squared error of these estimators. Finally recommendations have been made for the use of these estimators.
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