GENERALIZED INFERENCE FOR THE GAMMA DISTRIBUTION AND ITS APPLICATIONS

Abstract

The gamma distribution has been extensively used in a wide class of applications. Despite a multitude of studies in the literature, interval estimation of the gamma distribution tends to be difficult. Most existing methods have been found inaccurate given a small or moderate sample size. To bridge this gap, we first develop a general framework of interval estimation of the gamma distribution in this thesis. The key idea is based on the method of generalized pivotal quantity (GPQ). We then consider the application of the gamma distribution in various areas, including lifetime modelling, degradation modelling, quality control, and environmental monitoring. For each application, the gamma distribution is found to be useful and the GPQ method is used to construct some important statistical limits. Simulations are conducted to compare the proposed methods with the exiting methods. Illustrative examples are provided to demonstrate the proposed methods.