Abstract We derive an expression for the Spearman rank correlation of bivariate scale mixtures of normals (SMN) and we show that within this class, for any value of the correlation parameter, the Spearman rank correlation of the normal is the greatest in absolute value. We then provide expressions for the symmetric generalized hyperbolic, the Bessel, and the Laplace distributions. We further derive an expression for the Spearman rank correlation of the Student t distribution in terms of an easily computable one-dimensional integral, and we also consider the special case of the Cauchy. Finally, we show how our results can be used in a rank-based estimation of the parameters of the Student t distribution.

中文翻译：

---

双变量学生 t 的 Spearman 秩相关和正态分布的尺度混合

摘要 我们推导出了双变量标度法线混合 (SMN) 的 Spearman 秩相关表达式，并表明在该类中，对于相关参数的任何值，正态的 Spearman 秩相关绝对值最大。然后我们提供对称广义双曲线、贝塞尔和拉普拉斯分布的表达式。我们根据易于计算的一维积分进一步推导出学生 t 分布的 Spearman 秩相关表达式，并且我们还考虑了柯西的特殊情况。最后，我们展示了我们的结果如何用于学生 t 分布参数的基于等级的估计。