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 ($\mathcal{S}\mathcal{G}\mathcal{N}$) 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.

Keywords:

• Approximating binomial distribution
• Skew-normal
• Skew generalized normal
• Stochastic representation

2000 Mathematics Subject Classification:

• 62F03
• 62F10
• 62E99

Additional information

Funding

This work is based upon research supported by the National Research Foundation, South Africa (Grant number: 91497; 109214; 102640). Opinions expressed a conclusions arrived at in this study are those of the authors and are not necessarily attributed to the NRF.