Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions

Abstract

The skew-normal distribution was popularised by Azzalini [4] to model skewed data. However, the skew-normal distribution is always unimodal. Kundu [24] recently presented the geometric skew-normal distribution by considering a geometric compounding sum of normal random variables. This distribution is more flexible than the skew-normal distribution since it can be multimodal. In this dissertation we present a new distribution namely the geometric skew-Cauchy distribution. The idea follows a similar approach to that of Kundu's. The difference, however, is that we consider a geometric compounding sum of Cauchy random variables. The inclusion of a simulation and application chapter demonstrates the practical use of this new distribution. It turns out that the geometric skew-Cauchy distribution is also more flexible than the skew-normal distribution. It is concluded that this new distribution can be used as an alternative to the geometric skew-normal distribution since both distributions can be multimodal. The advantage over the geometric skew-normal distribution, is the ability of the geometric skew-Cauchy distribution to model fatter-tailed data.