Generalized Statistical Inference for Quantiles of Two-Parameter Gamma Distribution

Abstract

Gamma distribution is a widely used distribution to analyze data in many disciplines such as hydrology, meteorology, environmental monitoring, lifetime testing and reliability. In this study, we look at the statistical inference for the quantiles of two-parameter gamma distribution. The testing and estimation of gamma quantile are required especially in areas such as flood frequency analysis and life testing. For this problem, all the statistical inference methods available in the statistical literature are approximate methods. In this study, we propose two methods to tackle this problem. The first method is an exact statistical inference procedure utilizing the generalized p-value technique. The procedure is exact in the sense that it is based on exact probability statements rather than based on approximations. The second procedure is based on the parametric bootstrap approach. We apply the proposed methods to several examples with real data sets and compare the results with other existing methods. A limited simulation study is given to compare the performance of the proposed methods with other existing methods. Overall, according to the simulation results, in terms of size and power, these two new methods perform well over the other existing methods whether it is related to lower or higher quantiles.