  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 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.
