Modelling Skewed and Heavy-tailed Data Using a Normal Weighted Inverse Gaussian Distribution

Abstract

The normal distribution is inadequate in capturing skewed and heavy-tailed behaviour of data taken over short time intervals. In addition the data can be leptokurtic. For this reason a normal weighted inverse Gaussian distribution is proposed as an alternative to the normal inverse Gaussian distribution to handle such data. The mixing distribution used in the normal variance mean mixture is a finite mixture of two special cases of Generalized Inverse Gaussian \((\textit{GIG})\) distribution. The two special cases and the finite mixture are weighted inverse Gaussian distribution. The motivation for this work is that a finite mixture is more flexible than a single/standard distribution. The \(textit{EM}\)-algorithm has been used for parameter estimation.