We introduce the univariate two-piece sinh-arcsinh distribution, which contains two shape parameters that separately control skewness and kurtosis. We show that this new model can capture higher levels of asymmetry than the original sinh-arcsinh distribution (Jones and Pewsey, 2009), in terms of some asymmetry measures, while keeping the flexibility on the tails and tractability. The examples presented here illustrate that the two-piece sinh-arcsinh distribution has appealing inferential properties and emphasise the importance of using models with interpretable parameters. In all the examples, we compare the proposed distribution against appropriate competitors. Given that the normal distribution represents a particular case of the proposed model, the likelihood ratio test can be used to test normality. We present a simulation study showing that this test is very powerful, outperforming some popular competitors. Although we focus on the study of the univariate versions of the proposed distributions, we point out some multivariate extensions.
Statistical properties of the NSAS and skew-normal distributions can be found in REF .
On modelling asymmetric data using two-piece sinh-arcsinh distributions
arXiv: Applications
Mathematics