The multivariate slash and skew-slash student t distributions

In this article, we introduce the multivariate slash and skew-slash t distributions which provide alternative choices in simulating and fitting skewed and heavy tailed data. We study their relationships with other distributions and give the densities, stochastic representations, moments, marginal distributions, distributions of linear combinations and characteristic functions of the random vectors obeying these distributions. We characterize the skew t, the skew-slash normal and the skew-slash t distributions using both the hidden truncation or selective sampling model and the order statistics of the components of a bivariate normal or t variable. Density curves and contour plots are drawn to illustrate the skewness and tail behaviors. Maximum likelihood and Bayesian estimation of the parameters are discussed. The proposed distributions are compared with the skew-slash normal through simulations and applied to fit two real datasets. Our results indicated that the proposed skew-slash t fitting outperformed the skew-slash normal fitting and is a competitive candidate distribution in analyzing skewed and heavy tailed data.