The Gamma distribution is widely used in engineering and industrial applications. Hypothesis testing of the parameters is revisited in the two parameter Gamma distribution when both the parameters are unknown. The likelihood ratio test is implemented by simulating the distribution of the likelihood ratio statistic under the null hypothesis. A comparative study between the likelihood ratio test, the asymptotic likelihood ratio test, the Wald test, and the Score test is performed using simulation.

asymptotic likelihood ratio test, likelihood ratio test, Monte Carlo simulation, Score test, UMP test, Wald test.