circ_cor {BAMBI} | R Documentation |

## Sample circular correlation coefficients

### Description

Sample circular correlation coefficients

### Usage

```
circ_cor(
x,
type = "js",
alternative = "two.sided",
jackknife = FALSE,
bootse = FALSE,
n.boot = 100
)
```

### Arguments

`x` |
two column matrix. NA values are not allowed. |

`type` |
type of the circular correlation. Must be one of "fl", "js", "tau1" and "tau2". See details. |

`alternative` |
one of |

`jackknife` |
logical. Compute jackknifed estimate and standard error? Defaults to FALSE. |

`bootse` |
logical. Compute bootstrap standard error? Defaults to FALSE. |

`n.boot` |
number of bootstrapped samples to compute bootstrap standard error. Defaults to
100. Ignored if |

### Details

`circ_cor`

calculates the (sample) circular correlation between the columns of x.
Two parametric (the Jammalamadaka-Sarma (1988, equation 2.6) form `"js"`

, and
the Fisher-Lee (1983, Section 3) form `"fl"`

)
and two non-parametric (two versions of Kendall's tau) correlation coefficients are considered.
The first version of Kendall's tau (`"tau1"`

) is based on equation 2.1 in Fisher and Lee (1982),
whereas the second version (`"tau2"`

) is computed using equations 6.7-6.8 in Zhan et al (2017).

The cost-complexity for `"js"`

, `"fl"`

, `"tau2"`

and `"tau1"`

are `O(n), O(n^2), O(n^2)`

and `O(n^3)`

respectively, where `n`

denotes the number of rows in `x`

. As such, for large `n`

evaluation of
`"tau1"`

will be slow.

### References

Fisher, N. I. and Lee, A. J. (1982). Nonparametric measures of angular-angular association. Biometrika, 69(2), 315-321.

Fisher, N. I. and Lee, A. J. (1983). A correlation coefficient for circular data. Biometrika, 70(2):327-332.

Jammalamadaka, S. R. and Sarma, Y. (1988). A correlation coefficient for angular variables. Statistical theory and data analysis II, pages 349-364.

Zhan, X., Ma, T., Liu, S., & Shimizu, K. (2017). On circular correlation for data on the torus. Statistical Papers, 1-21.

### Examples

```
# generate data from vmsin model
set.seed(1)
dat <- rvmsin(100, 2,3,-0.8,0,0)
# now calculate circular correlation(s) between the 2 columns of dat
circ_cor(dat, type="js")
circ_cor(dat, type="fl")
circ_cor(dat, type="tau1")
circ_cor(dat, type="tau2")
```

*BAMBI*version 2.3.5 Index]