Multimodal and asymmetric bivariate circular data arise in several different disciplines and fitting appropriate distribution plays an important role in the analysis of such data. In this paper, we propose a new bivariate circular distribution which can be used to model both asymmetric and multimodal bivariate circular data simultaneously. In fact the proposed density covers unimodality as well as multimodality, symmetry as well as asymmetry of circular bivariate data. A number of properties of the proposed density are presented. A Bayesian approach with MCMC scheme is employed for statistical inference. Three real datasets and a simulation study are provided to illustrate the performance of the proposed model in comparison with alternative models such as finite mixture Cosine model.

中文翻译：

---

新的多峰不对称双变量圆分布

多峰和非对称双变量循环数据出现在几个不同的学科中，适合的适当分布在此类数据的分析中起着重要的作用。在本文中，我们提出了一种新的双变量圆分布，可用于同时建模非对称和多峰双变量圆数据。实际上，拟议的密度涵盖了单峰和多峰，圆形双变量数据的对称性和不对称性。提出了建议密度的许多特性。采用带有MCMC方案的贝叶斯方法进行统计推断。提供了三个实际数据集和一个仿真研究，以说明与有限混合余弦模型等替代模型相比，所提出模型的性能。