A Half-Circular Distribution on a Circle
Document Type
Article
Publication Date
1-1-2019
Abstract
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.
Keywords
Gamma distribution, Inverse stereographic projection, Maximum likelihood estimation, Trigonometric moments, Unimodality
Divisions
fac_med,MathematicalSciences
Funders
Universiti Teknologi MARA (UiTM) internal grant scheme, 600-IRMI/ PERDANA 5/3 BESTARI (042/2018)
Publication Title
Sains Malaysiana
Volume
48
Issue
4
Publisher
Penerbit Universiti Kebangsaan Malaysia