Skew-normal distributions : advances in theory and applications

Abstract

The normal distribution is popular in many statistical contexts. However, due to its symmetry and tail behavior it may not necessarily be the best choice to use in many real world applications. In order to alleviate the aforementioned issues, a symmetric generalised normal distribution that exhibits flexibility in its tail behavior is proposed as candidate to apply existing skewing methodology to. Methods to approximate the characteristics of this new distribution and a corresponding stochastic representation is derived. The skewed version of the generalised normal distribution, along with other distributions, is used in a distribution fitting context and to approximate particular binomial distributions as an application.