Abstract
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.
Additional information
Notes on contributors
Piao Chen
Mr. Chen is PhD Candidate in the Department of Industrial & Systems Engineering. His email address is [email protected].
Zhi-Sheng Ye
Dr. Ye is an Assistant Professor in the Department of Industrial & Systems Engineering. He is the corresponding author. His email is [email protected].