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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 origi- nal sinh-arcsinh distribution (Jones and Pewsey, 2009), in terms of some asym- m etry measures, while keeping the flexibility on the tails and tractability. We present an example using real data to illustrate the performance of the proposed model and compare it against appropriate competitors. Although we focus on the study of the univariate versions of the proposed distributions, we point out some multivariate extensions.

On modelling asymmetric data using two-piece sinh–arcsinh distributions