This paper studies circular correlations for the bivariate von Mises sine and cosine distributions. These are two simple and appealing models for bivariate angular data with five parameters each that have interpretations connected to those in the ordinary bivariate normal model. However, the variability and association of the angle pairs cannot be easily deduced from the model parameters unlike the bivariate normal. Thus to compute such summary measures, tools from circular statistics are needed. We derive analytic expressions and study the properties of the Jammalamadaka–Sarma and Fisher–Lee circular correlation coefficients for the von Mises sine and cosine models. Likelihood-based inference of these coefficients from sample data is then presented. The correlation coefficients are illustrated with numerical and visual examples, and the maximum likelihood estimators are assessed on simulated and real data, with comparisons to their non-parametric counterparts. Implementations of these computations for practical use are provided in our R package BAMBI.

本文研究了双变量 von Mises 正弦和余弦分布的循环相关性。这是两个简单且吸引人的二元角度数据模型，每个参数具有五个参数，其解释与普通二元正态模型中的参数相关。然而，与二元法线不同，角度对的可变性和关联性不能轻易地从模型参数中推断出来。因此，为了计算这样的汇总度量，需要来自循环统计的工具。我们推导出解析表达式并研究 von Mises 正弦和余弦模型的 Jammalamadaka-Sarma 和 Fisher-Lee 循环相关系数的性质。然后给出了从样​​本数据中对这些系数的基于似然的推断。相关系数用数字和视觉示例说明，最大似然估计量在模拟和真实数据上进行评估，并与它们的非参数对应物进行比较。我们的 R 包中提供了这些计算的实际使用实现小鹿斑比。