# On circular correlation for data on the torus

Xiaoping Zhan, Tiefeng Ma, Shuangzhe Liu, Kunio Shimizu

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The circular correlation topic for data on the torus is studied. Firstly, the order for two points on the circumference is considered and an order function is defined. Then, an alternative moment coefficient to measure T-linear association between two circular variables based on the order function is proposed. After the concordant on the torus is explained, an alternative rank correlation coefficient on the torus is also proposed. A number of properties for the two coefficients are investigated and their comparisons with the existing alternatives are made. Two examples of real data analysis are presented to illustrate our results.

Original language English 1827-1847 21 Statistical Papers 60 6 https://doi.org/10.1007/s00362-017-0897-5 Published - Dec 2019

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Torus
Alternatives
Spearman's coefficient
Circumference
Coefficient
Correlation coefficient
Data analysis
Moment
Coefficients
Rank correlation

### Cite this

Zhan, Xiaoping ; Ma, Tiefeng ; Liu, Shuangzhe ; Shimizu, Kunio. / On circular correlation for data on the torus. In: Statistical Papers. 2019 ; Vol. 60, No. 6. pp. 1827-1847.
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On circular correlation for data on the torus. / Zhan, Xiaoping; Ma, Tiefeng; Liu, Shuangzhe; Shimizu, Kunio.

In: Statistical Papers, Vol. 60, No. 6, 12.2019, p. 1827-1847.

Research output: Contribution to journalArticle

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T1 - On circular correlation for data on the torus

AU - Zhan, Xiaoping

AU - Ma, Tiefeng

AU - Liu, Shuangzhe

AU - Shimizu, Kunio

PY - 2019/12

Y1 - 2019/12

N2 - The circular correlation topic for data on the torus is studied. Firstly, the order for two points on the circumference is considered and an order function is defined. Then, an alternative moment coefficient to measure T-linear association between two circular variables based on the order function is proposed. After the concordant on the torus is explained, an alternative rank correlation coefficient on the torus is also proposed. A number of properties for the two coefficients are investigated and their comparisons with the existing alternatives are made. Two examples of real data analysis are presented to illustrate our results.

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KW - Circular data

KW - Circular order

KW - Kendall’s $$\tau$$τ

KW - T-linear

KW - Kendall’s τ

KW - Kendall's tau

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