dispersion: Circular distance and dispersion

In tectonicr: Analyzing the Orientation of Maximum Horizontal Stress

Circular distance and dispersion

Description

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.

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.

Value

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

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. \Sexpr[results=rd]{tools:::Rd_expr_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

b <- a + 90
circular_distance(a, b) # distance to multiple values

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)
circular_dispersion(sa.por$azi.PoR, y = 135, w = 1 / san_andreas$unc)

tectonicr documentation built on Sept. 11, 2024, 6:05 p.m.