Inference on the Gamma Distribution

This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for the gamma shape parameter is derived. The generalized confidence intervals for the rate parameter and other quantities such as mean are explored. The proposed generalized inferential procedures are extended to construct prediction limits for a single future measurement and for at least p of m measurements at each of r locations. The performance of the proposed procedures is evaluated using Monte Carlo simulation. The simulation results show that the proposed procedures are very satisfactory. Finally, three real examples are used to illustrate the proposed procedures. Supplementary materials for this article are available online.