Outlier detection in a new half-circular distribution

In this paper, we use a discordancy test based on spacing theory to detect outlier in a half-circular data. Up to now, numerous discordancy tests have been proposed to detect outlier in circular distributions which are defined in [0,2 pi]. However, some circular data lie within just half of this range. Therefore, first we introduce a new half-circular distribution developed using the inverse stereographic projection technique on a gamma distributed variable. Then, we develop a new discordancy test to detect single or multiple outliers in the half-circular data based on the spacing theory. We show the practical value of the test by applying it to an eye data set obtained from a glaucoma clinic at the University of Malaya Medical Centre, Malaysia.