TY - JOUR
ID - 4209
TI - An extension of the Cardioid distributions on circle
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN -
AU - Salavati, Erfan
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 45
EP - 52
KW - Circular Distributions
KW - Cardioid Distribution
KW - Von Mises Distribution
DO - 10.22060/ajmc.2020.18285.1029
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4209.html
L1 - https://ajmc.aut.ac.ir/article_4209_384f506c165ebe2a3d5dda21192cfab2.pdf
ER -