New results on comparisons of parallel systems with heterogeneous gamma components
Let \(X_1,X_2\) be two independent gamma random variables with \(X_i\) having the shape parameter \(r>0\) and the scale parameter \(\lambda_i\), \(i=1,2\). Let \(X_1^*,X_2^*\) be another pair of independent gamma random variables with \(X_i^*\) having the shape parameter \(r>0\) and the scale parameter \(\lambda_i^*\), \(i=1,2\). The authors find conditions on the four parameters \(\lambda_1,\lambda_2,\lambda_1^*,\lambda_2^*\) such that \(\max\{X_1,X_2\}\) and \(\max\{X_1^*,X_2^*\}\) are ordered with respect to the dispersive stochastic order. They also find two other sets of conditions on \(\lambda_1,\lambda_2,\lambda_1^*,\lambda_2^*\) such that \(\max\{X_1,X_2\}\) and \(\max\{X_1^*,X_2^*\}\) are ordered with respect to the star stochastic order.
scientific article; zbMATH DE number 5836631
scientific article