A unifying generator for cardioid modelling in circular statistics

Abstract

One of the most important distributions in the circular world is the cardioid distribution. This distribution, however, suffers limitations for multimodal or asymmetric occurrences in circular data. This study addresses this shortfall by developing a flexible cardioid generated class that can capture inherent skewness and multimodality that data might present. This class is obtained by expressing the density in a general form by making use of a measurable function termed as generator. Some of the existing extensions of the cardioid distribution is shown to be special cases of this class of cardioid-generator distribution, and flexible behaviour of the proposed class in terms of skewness and multimodality is graphically demonstrated. Special cases of new and existing models of the newly proposed class are compared by making use of simulation studies and data sets. The newly proposed cardioid-t distribution proved a worthy addition to the class of symmetric models, outperforming well known circular distributions in two of the real data applications presented here. Introducing a more flexible cardioid generated class opens new insights for the cardioid model and equips the practitioner with a modified set of tools towards uncovering the intricate world of directional statistics.