Approximate statistical limits for a gamma distribution

This study develops methods for constructing some important statistical limits of a gamma distribution. First, we construct upper prediction limits and tolerance limits for a gamma distribution. In addition, upper prediction limits for at least p of m measurements from a gamma distribution at each of r locations are constructed. This problem often arises in the field of environmental monitoring, as well as quality control. For each problem discussed in this study, the inferential procedure based on the generalized fiducial method is outlined and a simulation is conducted to assess its performance. Real data are used to demonstrate the proposed methods. In addition to the prediction and tolerance limits, our proposed methods can also be applied to the stress-strength problem involving two independent gamma random variables. Our investigation shows that the proposed methods perform uniformly well and they outperform existing methods.