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Circular Distance and Dispersion

Source: R/statistics.R
dispersion.Rd

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
)

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

circular_dispersion_alt(
  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.

Details

circular_distance_alt() and circular_dispersion_alt() are the alternative versions in Mardia and Jupp (2000), pp. 19-20. The alternative dispersion has a minimum at the sample median.

Note

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

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

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] 0.1495228
circular_dispersion(sa.por$azi.PoR, y = 135, w = 1 / san_andreas$unc)
#> [1] 0.09858997