Abstract We propose a flexible and interpretable framework for circular data, motivated by wind-direction regimes. The model is a covariate-dependent finite mixture of Kato–Jones (KJ) components, reparameterized so that each component is a convex combination of a wrapped–Cauchy core and a uniform background (a WC–uniform representation). This boundary–concentration form separates regime shape from diffuse transitional mass and, at the mixture level, induces a wrapped–Cauchy mixture with an explicit uniform background. Covariates such as hour of day and wind speed enter only through a multinomial-logit link on the mixture weights, so regime incidence varies with conditions while component locations and concentrations remain globally interpretable. On the theoretical side, we establish identifiability of the covariate-dependent WC–uniform mixture via a trigonometric-moment (Toeplitz/Carathéodory–Fejér) argument under mild ordering and compactness conditions, and we derive a likelihood-ratio test for the presence of a uniform background with a chi-bar-square limit, calibrated in practice by a parametric bootstrap. For estimation we develop a block-separable sieve EM algorithm that alternates a strictly concave multinomial-logit update for the weights with closed-form moment updates for the wrapped–Cauchy parameters, guaranteeing monotone ascent of the observed likelihood and convergence to stationary points. Simulation studies with and without covariates demonstrate accurate recovery of skewed, overlapping, and switching regimes, and highlight the robustness of the WC–uniform representation to diffuse noise. Applications to NOAA buoy wind directions show that the proposed framework provides interpretable regime and uniform-background diagnostics in multi-regime, transition-rich coastal settings, while also identifying cases in which simpler von Mises mixtures or kernel-based methods provide stronger predictive likelihood.
Abdolnasser Sadeghkhani (Wed,) studied this question.