A Kernel Scale Mixture of the Skew-Normal Distribution

The authors of this chapter provide a semi-parametric model for the skew-normal distribution by employing a kernel density estimator (KDE) as the mixing distribution. The objective of this strategy is to control the kurtosis of the distribution while maintaining the favorable characteristics of both the skew-normal density and the KDE. The importance of creating a semi-parametric skew-model is highlighted by simulation studies and a real data example. This model retains the key characteristics of the skew-normal distribution while including extra information from auxiliary observations.