Circular distance and dispersion

Circular distance between two angles and circular dispersion of angles about a specified angle.

Usage

circular_distance(x, y, axial = TRUE, na.rm = TRUE)

circular_dispersion(
  x,
  y = NULL,
  w = NULL,
  w.y = NULL,
  norm = FALSE,
  axial = TRUE,
  na.rm = TRUE
)

Arguments

x, y

vectors of numeric values in degrees. length(y) is either 1 or length(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. Whether NA values in x should be stripped before the computation proceeds.

w, w.y

(optional) Weights. A vector of positive numbers and of the same length as x. w.y is the (optional) weight of y.

norm

logical. Whether the dispersion should be normalized by the maximum possible angular difference.

Value

circular_distancereturns a numeric vector of positive numbers, circular_dispersionreturns a positive number.

Note

If from is NULL, than the circular variance is returned.

References

Mardia, K.V. (1972). Statistics of Directional Data: Probability and Mathematical Statistics. London: Academic Press.

See also

circular_mean(), circular_var().

Examples

a <- c(0, 2, 359, 6, 354)
circular_distance(a, 10) # distance to single value
#> [1] 0.030153690 0.019369152 0.036408073 0.004865966 0.075975952

b <- a + 90
circular_distance(a, b) # distance to multiple values
#> [1] 1 1 1 1 1

data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
circular_dispersion(sa.por$azi.PoR, y = 135)
#> [1] 0.1474684
circular_dispersion(sa.por$azi.PoR, y = 135, w = 1 / san_andreas$unc)
#> [1] 0.09840187