Exact statistical inference for quantities of loggamma distribution

Transformed gamma distributions are widely used in various fields such as survival analysis, reliability engineering, and environmental studies. Statistical inference for the quantities of the transformed gamma distributions is of great importance in these applications. However, traditional inference methods often rely on large sample approximations, which is not accurate for small sample sizes. To address this issue, we introduced an exact statistical inference framework for quantities of the transformed gamma distributions and applied the framework to loggamma distribution. The performance of the proposed framework was extensively evaluated via comprehensive simulation studies. The results showed that the proposed framework outperforms the parametric bootstrapping method in terms of coverage probability and type 1 error rate. Two real data applications are provided for illustrative purposes.