A Half-Circular Distribution on a Circle

Rambli, Adzhar and Mohamed, Ibrahim and Shimizu, Kunio and Ramli, Norlina Mohd (2019) A Half-Circular Distribution on a Circle. Sains Malaysiana, 48 (4). pp. 887-892. ISSN 0126-6039, DOI https://doi.org/10.17576/jsm-2019-4804-21.

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Official URL: 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.

Item Type: Article
Funders: Universiti Teknologi MARA (UiTM) internal grant scheme, 600-IRMI/ PERDANA 5/3 BESTARI (042/2018)
Uncontrolled Keywords: Gamma distribution; Inverse stereographic projection; Maximum likelihood estimation; Trigonometric moments; Unimodality
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
R Medicine
Divisions: Faculty of Medicine
Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 06 Feb 2020 01:22
Last Modified: 06 Feb 2020 01:22
URI: http://eprints.um.edu.my/id/eprint/23685

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