Assuming a two parameter gamma distribution to model the lifetime of a system we study the sampling distribution of three types of estimates of the model parameters, namely - (i) the maximum likelihood estimator (MLE); (ii) a bias corrected version of the MLE (BMLE); and (iii) a modified version of the MLE (MMLE). Existing literature provides some partial results about the bias and MSE of these estimators, but not much about their sampling distributions. In this investigation we go into details in observing the nature of the sampling distributions of the estimators through a comprehensive simulation study.

gamma distribution, maximum likelihood estimation, positively skewed distribution, bias, mean squared error.