Alternative discordancy test, Z a statistic for spherical data

This paper presents an alternative method for outlier detection in univariate spherical data via a discordancy test using Haversine distance. The test determines whether the value of the sum of Haversine distances for an outlier from a center point to every other point in the sample is significant. The efficiency of the newest Za statistic is verified using simulated data using the P5 performance measure, which proves its effectiveness, particularly for concentration parameters greater than 10. It is important to emphasize that this approach is very effective for large amounts of information. Since the Za statistic relies on the concentration parameters and the sample size, it is very flexible and versatile for different datasets wherein outlier detection is required. Some practical applications have been exploited, including outlier detection in eye data, dolerite magnetic remanence, and earthquake data. As for future applications, this method is flexible for future developments such as the usage of other distributions unlike the Fisher distribution increasing the range of applicability to various fields including geophysics, biology and seismology.