The gamma distribution is widely used in engineering and industrial applications. Hypothesis testing of the shape parameter is revisited in the two-parameter gamma distribution when the scale parameter is known. 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, the score test, and the small sample methods by Bhaumik et al. [1] and Bhaumik et al. [2] is performed using simulation.

arithmetic mean, digamma function, geometric mean, trigamma function.