A new measure of preferred direction for circular data using angular wrapping

IF 0.7 Q2 MATHEMATICS
Özge TEZEL, Buğra Kaan TİRYAKİ, Eda ÖZKUL, Orhan KESEMEN
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引用次数: 0

Abstract

The statistical techniques which are developed for the analysis of data in the linear number system cannot be applied to directional data directly. Circular data may be discontinuous in some principal interval. These discontinuities cause failure results in the circular statistics. Because of that the proposed wrapping operator must be used for data, which are defined in the discontinuous range. However, in both continuity and discontinuity, the wrapping operator works correctly. The most common preferred directions for circular data are circular mean and variance summarizing and comparing them. Although circular data has a very important role in statistics, the literature is weak in terms of statistical analysis of circular data. It creates a gap in this field. This study examines the preferred direction of circular data to fill this gap and presents a new measure of preferred direction for circular data using angular wrapping. Four different artificial and three real datasets are employed to evaluate the performance of the proposed methods. The results demonstrate the superiority of the proposed methods in terms of the absolute error and absolute percentage error. Consequently, it has been seen that the proposed methods giv e more consistent and more accurate results than thevectorial methods.
使用角包裹的圆形数据优选方向的新度量
为分析线性数字系统中的数据而开发的统计技术不能直接应用于定向数据。循环数据在某些主区间内可能是不连续的。这些不连续性导致循环统计中的失败结果。因此,建议的包装运算符必须用于在不连续范围内定义的数据。然而,在连续性和非连续性情况下,包裹运算符都能正常工作。对于循环数据,最常见的首选方向是循环均值和方差,对它们进行汇总和比较。虽然循环数据在统计学中有着非常重要的作用,但是在循环数据的统计分析方面文献较少。它在这个领域造成了一个空白。本研究考察了圆形数据的首选方向,以填补这一空白,并提出了使用角包裹的圆形数据的首选方向的新措施。采用四个不同的人工数据集和三个真实数据集来评估所提出方法的性能。结果表明,所提方法在绝对误差和绝对百分比误差方面具有优越性。因此,所提出的方法比向量方法给出了更一致和更准确的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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