Paper detail

An Extension of the Cardioid Distributions on Circle

A new family of distributions on the circle is introduced which are a generalization of the Cardioid distributions. The elementary properties such as mean, variance and the characteristic function are computed. The distribution is either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property.