The analysis of circular data is the main subject in many disciplines, such as meteorology and oceanography. In this article, we introduce a new multimodal skew‐circular model as an extension of the circular beta distribution. We propose a truncated power smoothing spline for modeling the skewness parameter and identifying significant factors of the asymmetry. A Markov chain Monte Carlo scheme is provided to perform statistical inference from a Bayesian perspective. Then, the performance of our modeling methodology to analyze specific circular responses is assessed through several simulation studies. To illustrate the usefulness of the new model in practical applications, we analyze measurements on the wind and wave directions in Norway. We also fit various regression models to show that the cubic smoothing spline approach performs better than competitive models in practical applications. Findings, based on prediction values, confirm that the proposed model can reasonably fit multimodal skewed‐circular responses.

中文翻译：

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多峰和斜圆响应的平滑样条模型：在气象学和海洋学中的应用

循环数据的分析是许多学科的主要学科，例如气象学和海洋学。在本文中，我们介绍了一种新的多峰偏斜圆形模型，作为圆形beta分布的扩展。我们提出了一个截断的功率平滑样条，用于建模偏度参数并确定不对称性的重要因素。提供了马尔可夫链蒙特卡洛方案，以从贝叶斯角度执行统计推断。然后，通过一些模拟研究评估了我们的建模方法分析特定循环响应的性能。为了说明新模型在实际应用中的实用性，我们分析了挪威风向和海浪方向的测量结果。我们还拟合了各种回归模型，以表明三次平滑样条曲线方法在实际应用中的性能优于竞争模型。根据预测值的发现，证实所提出的模型可以合理地拟合多模态斜圆形响应。