Title: Mastering the body and tail shape of a distribution
Authors: Andriette Bekker - University of Pretoria (South Africa)
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Matthias Wagener - University of Pretoria (South Africa) [presenting]
Abstract: The normal distribution and its perturbations have 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 which enables the visualization and control of the body and the tail shape separately. This provides a flexible modelling opportunity with an emphasis on parameter inference and interpretation. Two related models, the two-piece body-tail generalised normal (TPBTGN) and the two-piece tail adjusted normal (TPTAN) are swiftly introduced to demonstrate this potential. This flexible modelling methodology is then demonstrated on heavy and light-tailed data.