A Half-Circular Distribution on a Circle

• Main Authors: Rambli, Adzhar, Mohamed, Ibrahim, Shimizu, Kunio, Ramli, Norlina Mohd
• Format: Article
• Published: Penerbit Universiti Kebangsaan Malaysia 2019
• Subjects: QA Mathematics; QA75 Electronic computers. Computer science; R Medicine
• Online Access: http://eprints.um.edu.my/23685/; https://doi.org/10.17576/jsm-2019-4804-21

Up to now, circular distributions are defined in [0,2 π), except for axial distributions on a semicircle. However, some circular data lie within just half of this range and thus may be better fitted by a half-circular distribution, which we propose and develop in this paper using the inverse stereographic projection technique on a gamma distributed variable. The basic properties of the distribution are derived while its parameters are estimated using the maximum likelihood estimation method. We show the practical value of the distribution by applying it to an eye data set obtained from a glaucoma clinic at the University of Malaya Medical Centre, Malaysia. © 2019 Penerbit Universiti Kebangsaan Malaysia. All rights reserved.