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

We introduce the univariate two-piece sinh–arcsinh distribution, which contains two shape parameters that separately control skewness and kurtosis.We show that this newmodel can capture higher levels of asymmetry than the original sinh–arcsinh distribution [Biometrika 96 (2009) 761–780], in terms of some asymmetry measures, while keeping flexibility of the tails and tractability. We illustrate the performance of the proposed model with real data, and compare it to appropriate alternatives. Although we focus on the study of the univariate versions of the proposed distributions, we point out some multivariate extensions.