Computational methods applied to a skewed generalized normal family

Abstract

Some characteristics of the normal distribution may not be ideal to model in many applications. We develop a skew generalized normal (SGN) distribution by applying a skewing method to a generalized normal distribution, and study some meaningful statistical characteristics. Computational methods to approximate, and a well-constructed efficient computational approach to estimate these characteristics, are presented. A stochastic representation of this distribution is derived and numerically implemented. The skewing method is extended to the elliptical class resulting in a more general framework for skewing symmetric distributions. The proposed distribution is applied in a fitting context and to approximate particular binomial distributions.