Calculate the (weighted median) and standard deviation of orientation data.
Usage
circular_mean(x, w = NULL, axial = TRUE, na.rm = TRUE)
circular_var(x, w = NULL, axial = TRUE, na.rm = TRUE)
circular_sd(x, w = NULL, axial = TRUE, na.rm = TRUE)
circular_median(x, w = NULL, axial = TRUE, na.rm = TRUE)
circular_quantiles(x, w = NULL, axial = TRUE, na.rm = TRUE)
circular_IQR(x, w = NULL, axial = TRUE, na.rm = TRUE)
sample_circular_dispersion(x, w = NULL, axial = TRUE, na.rm = TRUE)Arguments
- x
numeric vector. Values in degrees.
- w
(optional) Weights. A vector of positive numbers and of the same length as
x.- axial
logical. Whether the data are axial, i.e. pi-periodical (
TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).- na.rm
logical value indicating whether
NAvalues inxshould be stripped before the computation proceeds.
Note
Weighting may be the reciprocal of the data uncertainties.
Weightings have no effect on quasi-median and quasi-quantiles if
length(x) %% 2 != 1 and length(x) %% 4 == 0, respectively.
References
Mardia, K.V. (1972). Statistics of Directional Data: Probability and Mathematical Statistics. London: Academic Press.
Mardia, K.V., and Jupp, P.E (1999). Directional Statistics, Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., Hoboken, NJ, USA. doi:10.1002/9780470316979
Ziegler, M. O.; Heidbach O. (2019). Manual of the Matlab Script Stress2Grid v1.1. WSM Technical Report 19-02, GFZ German Research Centre for Geosciences. doi:10.2312/wsm.2019.002
Heidbach, O., Tingay, M., Barth, A., Reinecker, J., Kurfess, D., & Mueller, B. (2010). Global crustal stress pattern based on the World Stress Map database release 2008. Tectonophysics 482, 3<U+2013>15, doi:10.1016/j.tecto.2009.07.023
Examples
x <- rvm(10, 0, 100) %% 180
unc <- stats::runif(100, 0, 10)
circular_mean(x, 1 / unc)
#> [1] 0.6221128
circular_var(x, 1 / unc)
#> [1] 0.01727118
circular_sd(x, 1 / unc)
#> [1] 5.347582
circular_median(x, 1 / unc)
#> [1] 172.0181
circular_quantiles(x, 1 / unc)
#> 25% 50% 75%
#> 5.704103 172.018116 178.181497
circular_IQR(x, 1 / unc)
#> [1] 7.522606
data("san_andreas")
circular_mean(san_andreas$azi)
#> [1] 10.64134
circular_mean(san_andreas$azi, 1 / san_andreas$unc)
#> [1] 9.98401
circular_median(san_andreas$azi)
#> [1] 35.5
circular_median(san_andreas$azi, 1 / san_andreas$unc)
#> [1] 35.62501
circular_quantiles(san_andreas$azi)
#> 25% 50% 75%
#> 15.0 35.5 160.0
circular_quantiles(san_andreas$azi, 1 / san_andreas$unc)
#> 25% 50% 75%
#> 15.00000 35.62501 160.00000
circular_var(san_andreas$azi)
#> [1] 0.3177094
circular_var(san_andreas$azi, 1 / san_andreas$unc)
#> [1] 0.201883
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
circular_mean(sa.por$azi.PoR, 1 / san_andreas$unc)
#> [1] 138.9025
circular_median(sa.por$azi.PoR, 1 / san_andreas$unc)
#> [1] 136.8581
circular_var(sa.por$azi.PoR, 1 / san_andreas$unc)
#> [1] 0.1896731
circular_quantiles(sa.por$azi.PoR, 1 / san_andreas$unc)
#> 25% 50% 75%
#> 124.8436 136.8581 150.2225