The experiment is to generate a random sample \(\boldsymbol{X} = (X_1, X_2, \ldots, X_n)\) of size \(n\) from the gamma distribution with shape parameter \(k\) and scale parameter \(b\). The statistics of interest are \[ U = \frac{M^2}{T^2}, \quad V = \frac{T^2}{M}, \quad U_b = \frac{M}{b}, \quad V_k = \frac{M}{k} \] where \[ M = \frac{1}{n} \sum_{i=1}^n X_i, \quad T^2 = \frac{1}{n} \sum_{i=1}^n (X_i - M)^2 \] Statistic \(U\) is an estimator of \(k\) and statistic \(V\) is an estimator of \(b\). Statistic \(U_b\) is an estimator of \(k\) assuming that \(b\) is known, and \(V_k\) is an estimator of \(b\) with \(k\) known. The parameters \(k\), \(b\), and \(n\) can be varied with the input controls.