Mark Variogram
Estimate the mark variogram of a marked point pattern.
markvario(X, correction = c("isotropic", "Ripley", "translate"),
r = NULL, method = "density", ..., normalise=FALSE)X |
The observed point pattern.
An object of class |
correction |
A character vector containing any selection of the
options |
r |
numeric vector. The values of the argument r at which the mark variogram gamma(r) should be evaluated. There is a sensible default. |
method |
A character vector indicating the user's choice of
density estimation technique to be used. Options are
|
... |
Other arguments passed to |
normalise |
If |
The mark variogram gamma(r) of a marked point process X is a measure of the dependence between the marks of two points of the process a distance r apart. It is informally defined as
gamma(r) = E[(1/2) * (M1 - M2)^2 ]
where E[ ] denotes expectation and M1,M2 are the marks attached to two points of the process a distance r apart.
The mark variogram of a marked point process is analogous, but not equivalent, to the variogram of a random field in geostatistics. See Waelder and Stoyan (1996).
An object of class "fv" (see fv.object).
Essentially a data frame containing numeric columns
r |
the values of the argument r at which the mark variogram gamma(r) has been estimated |
theo |
the theoretical value of gamma(r) when the marks attached to different points are independent; equal to the sample variance of the marks |
together with a column or columns named
"iso" and/or "trans",
according to the selected edge corrections. These columns contain
estimates of the function gamma(r)
obtained by the edge corrections named.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Cressie, N.A.C. (1991) Statistics for spatial data. John Wiley and Sons, 1991.
Mase, S. (1996) The threshold method for estimating annual rainfall. Annals of the Institute of Statistical Mathematics 48 (1996) 201-213.
Waelder, O. and Stoyan, D. (1996) On variograms in point process statistics. Biometrical Journal 38 (1996) 895-905.
Mark correlation function markcorr for numeric marks.
Mark connection function markconnect and
multitype K-functions Kcross, Kdot
for factor-valued marks.
# Longleaf Pine data
# marks represent tree diameter
data(longleaf)
# Subset of this large pattern
swcorner <- owin(c(0,100),c(0,100))
sub <- longleaf[ , swcorner]
# mark correlation function
mv <- markvario(sub)
plot(mv)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.