The hue and chroma components of an image pixel carry crucial information that can be exploited to perform segmentation. However, due to its directional property, a circular distribution is required to characterize the hue component. In this article, we propose a mixture of bi-variate circular linear distributions, for modelling hue and chroma information. The proposed model incorporates a joint distribution of a circular and a linear variable by means of circular copula and offers a flexible architecture that deals with heterogeneous margins for different mixture components. We apply this model for psoriatic plaque segmentation in skin images, using the hue and the chroma information. We observe that the chroma exhibits a heterogeneous distribution in a skin image. Moreover, the joint distribution of hue and chroma possesses multi-modal characteristics. Our model is suitable to perform segmentation under such circumstances. After segmentation, we perform automatic plaque localization by means of a statistical model that exploits hue information of the segmented regions. We conduct the experiments on a set of 75 psoriasis skin images. Both segmentation and localization performances are evaluated with respect to a number of commonly used criteria. The experimental results show that the proposed segmentation model outperforms several competing supervised and unsupervised methods in detecting psoriatic plaque regions in skin images.