ripk

Ripley’s K function

R

ripk(x, y = NULL, win, r, corr = "iso", metric = "euclid")

Ripley’s K function of a point pattern in the rectangle win at radii r, and Besag’s L = sqrt(K / pi). Under complete spatial randomness K(r) = pi r^2 and L(r) = r. Four estimators: "none" (no edge correction), "border" (only points at least r from the edge are centres), "modif" (the modified border estimator, with the area of the eroded window; NaN once r reaches half a side) and "iso" (Ripley’s isotropic correction, each pair weighted by the inverse of the share of the circle through the other point that lies in the rectangle, computed exactly). The normalisation is n (n - 1), as in spatstat.

Parameters

x, y

The points in planar coordinates (project longitude and latitude with eqproj() first): x and y numeric vectors of equal length, or x a matrix or data frame with columns named x and y (an unnamed two-column matrix is read as x then y). At least two points, all inside win; no missing values.

win

The study rectangle c(xmin, xmax, ymin, ymax), in the unit of the coordinates. The intensity is the number of points over its area.

r

The radii: non-negative numbers in strictly increasing order, in the unit of the coordinates.

corr

The edge correction: "iso", "border", "modif" or "none".

metric

The distance: "euclid" or "manhattan" (|dx| + |dy|, a street grid aligned with the axes), as in spwt() and jtsurf(). Under Manhattan distance K(r) = 2 r^2 and L = sqrt(K / 2) under randomness; the border and modified border corrections carry over (a Manhattan ball of radius r lies in the rectangle exactly when its centre is at least r from every edge), while the isotropic correction, the share of a circle, has no Manhattan form and is refused.

Returns

A data frame with one row per radius: r, k (in the square of the coordinates’ unit) and l (sqrt(k / pi), or sqrt(k / 2) under Manhattan distance).

References

Ripley, B. D. (1976). The second-order analysis of stationary point processes. Journal of Applied Probability, 13(2), 255-266. doi:10.2307/3212829

Ripley, B. D. (1977). Modelling spatial patterns. Journal of the Royal Statistical Society, Series B, 39(2), 172-212. doi:10.1111/j.2517-6161.1977.tb01615.x

Examples

set.seed(1)
ripk(runif(100), runif(100), win = c(0, 1, 0, 1), r = seq(0, 0.25, 0.05))

Generated from the R help page: ripk in the R reference.