Mark variogram

\(\gamma(r) = E((m_i - m_j)^2/2 | d_{ij} = r)\), as spatstat.explore::markvario: the smoother of MarkCorrelation with \(f = (m_1 - m_2)^2/2\) and no normalisation; under independent marks it equals the mark variance.

Usage

MarkVariogram(points, marks, window, r = NULL, rmax = NULL, correction = "iso")

Arguments

points

Two-column matrix of coordinates.

marks

Non-negative numeric marks.

window

c(xmin, xmax, ymin, ymax).

r

Distances (default 513 values up to the Kest rmax rule).

rmax

Largest distance for the default r.

correction

"iso" or "trans".

Value

List with r, gamma, bw, theo.

Examples

P <- cbind(c(.1, .4, .35, .8, .7, .55, .2, .9, .15, .6), c(.2, .8, .3, .6, .15, .5, .65, .9,
  .95, .85))
MarkVariogram(P, c(1, 2, 1.5, 3, .5, 2.5, 1, 2, .8, 1.2), c(0, 1, 0, 1))$gamma[257]
#> [1] 0.32