标题： 通过非中心偏t分布对多变量偏斜和厚尾数据进行灵活建模：应用于肿瘤形状数据 显示英文标题

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

摘要： 我们提出了一种多元非中心偏t（NCST）分布的灵活公式，该分布通过用独立的卡方变量缩放偏正态随机向量来定义。这种构造通过允许不对称性和非中心性，扩展了经典的多元t族，为现有的偏t模型提供了一个替代方案，这些模型通常依赖于可处理性的限制性假设。我们推导了NCST分布的关键理论性质，包括其矩结构、仿射变换行为以及二次形式的分布。由于缺乏闭合形式的密度，我们实施了蒙特卡洛似然近似以实现最大似然估计，并通过模拟研究评估其性能。为了展示实际效用，我们将NCST模型应用于乳腺癌诊断数据，对肿瘤形状的多个特征进行建模。根据信息准则和视觉诊断，NCST模型在存在偏度和厚尾的情况下相比标准替代方案（包括多元正态、偏正态和Azzalini的偏$t$分布）表现出更优的拟合效果。我们的研究结果表明，NCST分布为建模复杂多元数据提供了一个有用且可解释的选择，这突显了在似然推断、贝叶斯计算以及涉及不对称性和非高斯依赖性的应用中的未来发展方向。 显示英文摘要

摘要： We propose a flexible formulation of the multivariate non-central skew t (NCST) distribution, defined by scaling skew-normal random vectors with 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, which includes its moment structure, affine transformation behavior, and the distribution of quadratic forms. Due to the lack of a closed-form density, we implement a Monte Carlo likelihood approximation to enable maximum likelihood estimation and evaluate its performance through simulation studies. 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 based on 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 $t$ distribution. 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.