  We introduce a new family of multivariate distributions by taking the
component-wise Tukey-h transformation of a random vector following a
skew-normal distribution. The proposed distribution is named the
skew-normal-Tukey-h distribution and is an extension of the skew-normal
distribution for handling heavy-tailed data. We compare this proposed
distribution to the skew-t distribution, which is another extension of the
skew-normal distribution for modeling tail-thickness, and demonstrate that when
there are substantial differences in marginal kurtosis, the proposed
distribution is more appropriate. Moreover, we derive many appealing stochastic
properties of the proposed distribution and provide a methodology for the
estimation of the parameters in which the computational requirement increases
linearly with the dimension. Using simulations, as well as a wine and a wind
speed data application, we illustrate how to draw inferences based on the
multivariate skew-normal-Tukey-h distribution.
