Kmulti.ls {ecespa} | R Documentation |
Lotwick's and Silverman's combined estimator of the marked K-function
Description
For a multitype point pattern, calculates the combined estimator of the bivariate Kij(r)
and Kji(r)
functions.
Usage
Kmulti.ls(X, I, J, r = NULL, corre = "isotropic")
Arguments
X |
Multitype marked point pattern. An object with the |
I |
Subset index specifying the points of the first pattern. |
J |
Subset index specifying the points of the second pattern. |
r |
Numeric vector. The values of the argument r at which the multitype K function |
corre |
A character item selecting any of the options "border", "bord.modif", "isotropic", "Ripley" or
"translate", as described in |
Details
As a consequence of edge effects, the estimators Kij(r)
and Kji(r)
of the same bivariate pattern could differ.
K^*ij(r)
is the combined estimator defined by Lotwick and Silverman (1982) as
nj*Kij(r)+ ni*Kji(r) / (ni + nj) ,
ni
and nj
being respectively the number of points in I
and J
.
Value
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 function |
.
theo |
The theoretical value of |
.
together with a column or columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections.
These columns contain estimates of the function K^*ij(r)
obtained by the edge corrections named.
Note
Kmulti.ls
is a wrapper for a convenient use of the Kmulti
function of spatstat.
Please refer to its help page for additional documentation.
Author(s)
Marcelino de la Cruz
References
Lotwick,H.W. & Silverman, B. W. 1982. Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society B, 44: 406-413. doi:10.1111/j.2517-6161.1982.tb01221.x.
Examples
data(amacrine)
plot(Kmulti.ls(amacrine, I=amacrine$marks=="on", J=amacrine$marks=="off",
corre="isotropic"), sqrt(./pi)-r~r, main="")
# compare with Kmulti
plot(Kmulti(amacrine, I=amacrine$marks=="on", J=amacrine$marks=="off"),
sqrt(iso/pi)-r~r, add=TRUE, col=3)
plot(Kmulti(amacrine, J=amacrine$marks=="on", I=amacrine$marks=="off"),
sqrt(iso/pi)-r~r, add=TRUE, col=4)