A smoothing spline model for multimodal and skewed circular responses: Applications in meteorology and oceanography

Abstract

AbstractThe 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.