Abstract

Circular data—such as directions, angles, and other measurements on the unit circle—often include unusual observations that can distort classical statistical inference. We introduce a model-based framework for robust circular data analysis that distinguishes between different forms of departure from a reference model. Starting with a symmetric, unimodal reference distribution, we develop a family of finite mixture models that captures both mild and gross anomalies, either separately or simultaneously. The framework classifies observations automatically, without relying on arbitrary thresholds, while providing interpretable summaries of anomaly prevalence and dispersion. We demonstrate the approach using standard circular distributions and evaluate its performance through simulation studies and applications to environmental data. Our results show that modelling multiple types of anomalies jointly can improve model fit and reveal how different components contribute to the observed data. More broadly, this work highlights the value of mixture-based robust methods not only for detecting anomalies, but also for uncovering and interpreting latent structure in circular data.