On Bias Corrected Estimators of the Two Parameter Gamma Distribution

The gamma distribution, which is a member of Pearson Type III family of distributions, is one of the most commonly used distribution in engineering applications since it can be used as a probability model for positive data sets exhibiting various degrees of skewness. The maximum likelihood estimators (MLE) of the two parameter gamma distribution are known to be biased, and bias-corrected estimators of the parameters are available in the literature. In this paper, we have used Monte-Carlo simulation to estimate the bias and mean squared error (MSE) of the moment estimators, the ML estimators, and bias-corrected ML estimators. Our simulations show that the bias-correction available in the literature fails to remove the bias in the MLE for small values of the shape parameter.