Mastering the body and tail shape of a distribution

Abstract: The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to distinguish between changes in the relative body and tail shapes when using these generalizations. What we propose is a neat integration approach generalization which enables the visualization and control of the body and the tail shape separately. This provides a flexible modeling opportunity with an emphasis on parameter inference and interpretation. Two related models, the two-piece body-tail generalized normal and the two-piece tail adjusted normal are swiftly introduced to demonstrate this inferential potential. The methodology is then demonstrated on heavy and light-tailed data.