Title: A more general framework for the skew normal distributions
Authors: Andriette Bekker - University of Pretoria (South Africa) [presenting]
BW Rowland - University of Pretoria (South Africa)
JT Ferreira - University of Pretoria (South Africa)
Mohammad Arashi - Ferdowsi University of Mashhad (Iran)
Abstract: The normal distribution is popular in many statistical contexts. However it is rather restrictive to apply to real world applications due to its symmetry and tail behaviour. In order to alleviate the aforementioned issues, a generalised normal distribution that exhibits flexibility in its tail behaviour is proposed as candidate to apply existing skewing methodology to. Methods to approximate the characteristics of this skew generalised-normal type I distribution (SGNI) and a corresponding stochastic representation are presented. The existing skewing methodology is extended to the elliptical class with the generalised normal distribution as the symmetric base. Furthermore, this SGNI distribution, along with other competing distributions (normal and skew- normal), is used in a distribution fitting context. In the landscape of skew distributions, this new SGNI distribution outperforms existing competing distributions, specifically in approximating particular binomial distributions when $p$ not equal to 0.5.