Sample circular dispersion

Alternative versions of variance, dispersion a distance (Mardia and Jupp, 1999; pp. 19-20). These alternative dispersion has a minimum at the sample median.

Usage

sample_circular_variance(x, w = NULL, axial = TRUE, na.rm = TRUE)

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

sample_circular_dispersion(
  x,
  y = NULL,
  w = NULL,
  w.y = NULL,
  axial = TRUE,
  na.rm = TRUE
)

Arguments

x, y

vectors of numeric values in degrees. length(y) is either 1 or length(x)

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.

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.

References

N.I. Fisher (1993) Statistical Analysis of Circular Data, Cambridge University 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

Examples

a <- c(0, 2, 359, 6, 354)
sample_circular_distance(a, 10) # distance to single value
#> [1] 5.0 4.0 5.5 2.0 8.0

b <- a + 90
sample_circular_distance(a, b) # distance to multiple values
#> [1] 45 45 45 45 45

data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
sample_circular_variance(sa.por$azi.PoR)
#> [1] 0.6037799
sample_circular_dispersion(sa.por$azi.PoR, y = 135)
#> [1] 10.88795
sample_circular_dispersion(sa.por$azi.PoR, y = 135, w = 1 / san_andreas$unc)
#> [1] 8.233385