ecespa (version 1.1-17)

Kmulti.ls: 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")

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 \(K^*ij(r)\) has been estimated

.

theo

The theoretical value of \(K*ij(r)\) for a marked Poisson process, namely \(pi * r^2\)

.

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.

Arguments

X

Multitype marked point pattern. An object with the ppp format of spatstat.

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 \(K^*ij(r)\) should be evaluated.

corre

A character item selecting any of the options "border", "bord.modif", "isotropic", "Ripley" or "translate", as described in Kest. It specifies the edge correction(s) to be applied.

Author

Marcelino de la Cruz

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 \(J\).

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. tools:::Rd_expr_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)