Test for Uniformity of Exchangeable Random Variables on the Circle
- Authors
- Cho, Seonghun; Choi, Young-Geun; Lim, Johan; Lee, Won Jun; Bai, Hyun-Jeong; Kwon, Sungwon
- Issue Date
- Jun-2021
- Publisher
- 한국통계학회
- Keywords
- Exchangeability; Flocking behavior; Kuiper’s test; Normalized infinitely divisible distribution; Termite; Uniformity on the circle
- Citation
- Journal of the Korean Statistical Society, v.50, no.2, pp 615 - 630
- Pages
- 16
- Journal Title
- Journal of the Korean Statistical Society
- Volume
- 50
- Number
- 2
- Start Page
- 615
- End Page
- 630
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/1058
- DOI
- 10.1007/s42952-020-00092-3
- ISSN
- 1226-3192
1876-4231
- Abstract
- We are motivated by our laboratory experiment on the flocking behavior of termites. To test for the existence of flocking behavior, we revisit the problem to test uniform samples (with the samples uniformly distributed) on the circle. Unlike most existing works, we assume that the samples are exchangeably dependent. We consider the class of normalized infinitely divisible distributions for the spacings of the samples, which form uniform samples on the circle. To test the uniformity, we study a test (Kuiper’s test) based on spacings of the samples and compute the asymptotic null distribution of the test statistic as the scaled Kolmogorov distribution. We apply the procedure to our experimental data and justify the flocking behavior of termites. © 2020, Korean Statistical Society.
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