A Modified Gamma Model: Properties, Estimation, and Applications

Abstract

Statistical methods are essential for describing, predicting, and modeling natural phenomena in numerous application areas. These methods are helpful for modeling and predicting data in medicine, reliability engineering, actuarial science, and other fields. This paper presents a novel, simple, and fully flexible modified gamma model. The new model provides various forms of densities, including symmetric, asymmetric, unimodal, and reversed-J shapes, as well as a bathtub-shaped failure rate, which is suitable for modeling the lifespan of patients with an increased risk of death. Some basic and dynamic properties of the model are examined. Four methods for estimating its parameters are discussed, and a simulation study is used to examine the consistency and efficiency of these estimators. Finally, the usefulness of the proposed model is demonstrated in the analysis of some data sets.