An extension of the Cardioid distributions on circle

Document Type : Original Article


Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran



A new family of distributions on the circle is introduced which is a generalization of the Cardioid distributions‎. ‎The elementary properties such as mean‎, ‎variance, and the characteristic function are computed‎. ‎The distribution is shown to be 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)‎. ‎This implies that the estimation problem is well-defined. 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. Finally‎, ‎we study the maximum likelihood estimation for this family.‎


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