Flexible Modeling of Multivariate Skewed and Heavy-Tailed Data via a Non-Central Skew t Distribution with Application to Tumor Shape Data

Abstract We propose a non-central formulation of the multivariate skew t (NCST) distribution, defined by scaling skew normal random vectors by independent chi-squared variables. This construction extends the classical multivariate t family by allowing both asymmetry and non-centrality, which provides an alternative to existing skew t models that often rely on restrictive assumptions for tractability. We derive key theoretical properties of the NCST distribution, including its moment structure, behavior under affine transformations, and the distribution of quadratic forms. To demonstrate practical utility, we apply the NCST model to breast cancer diagnostic data, modeling multiple features of tumor shape. The NCST model achieves a superior fit, as indicated by information criteria and visual diagnostics, particularly in the presence of skewness and heavy tails, compared to standard alternatives, including the multivariate normal, skew normal, and Azzalini’s skew t distributions. Our findings suggest that the NCST distribution offers a useful and interpretable choice for modeling complex multivariate data, which highlights promising directions for future development in likelihood inference, Bayesian computation, and applications involving asymmetry and non-Gaussian dependence.