Abstract Circular data are encountered throughout a variety of scientific disciplines, such as in eye movement research as the direction of saccades. Motivated by such applications, mixtures of peaked circular distributions are developed. The peaked distributions are a novel family of Batschelet-type distributions, where the shape of the distribution is warped by means of a transformation function. Because the Inverse Batschelet distribution features an implicit inverse that is not computationally feasible for large or complex data, an alternative called the Power Batschelet distribution is introduced. This distribution is easy to compute and mimics the behavior of the Inverse Batschelet distribution. Inference is performed in both the frequentist framework, through Expectation–Maximization (EM) and the bootstrap, and the Bayesian framework, through MCMC. All parameters can be fixed, which may be done by assumption to reduce the number of parameters. Model comparison can be performed through information criteria or through bridge sampling in the Bayesian framework, which allows performing a wealth of hypothesis tests through the Bayes factor. An R package, flexcircmix , is available to perform these analyses.

中文翻译：

---

应用于跳视方向的圆形数据的峰值功率 Batschelet 分布的混合

摘要 循环数据在各种科学学科中都会遇到，例如在作为扫视方向的眼动研究中。受此类应用的启发，开发了尖峰圆形分布的混合物。峰值分布是一个新的 Batschelet 型分布族，其中分布的形状通过转换函数进行扭曲。由于 Inverse Batschelet 分布具有隐式逆，对于大型或复杂数据在计算上不可行，因此引入了一种称为 Power Batschelet 分布的替代方案。这种分布很容易计算并且模仿了 Inverse Batschelet 分布的行为。推理在频率论框架中执行，通过期望最大化（EM）和引导程序，以及贝叶斯框架，通过 MCMC。所有参数都可以固定，这可以通过假设来减少参数的数量。模型比较可以通过信息标准或通过贝叶斯框架中的桥采样进行，这允许通过贝叶斯因子进行大量的假设检验。R 包 flexcircmix 可用于执行这些分析。