spatstat.explore (version 3.7-0)

localKcross.inhom: Inhomogeneous Multitype K Function

Description

Computes spatially-weighted versions of the the local multitype \(K\)-function or \(L\)-function.

Usage

localKcross.inhom(X, from, to,
              lambdaFrom=NULL, lambdaTo=NULL,
              ..., rmax = NULL,
              correction = "Ripley", sigma=NULL, varcov=NULL,
              lambdaX=NULL, update=TRUE, leaveoneout=TRUE)
  localLcross.inhom(X, from, to,
              lambdaFrom=NULL, lambdaTo=NULL, ..., rmax = NULL)

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv. Essentially a data frame containing columns

r

the vector of values of the argument \(r\) at which the function \(K\) has been estimated

theo

the theoretical value \(K(r) = \pi r^2\) or \(L(r)=r\) for a stationary Poisson process

together with columns containing the values of the neighbourhood density function for each point in the pattern of type from. The last two columns contain the r and theo values.

Details

The functions localKcross.inhom and localLcross.inhom are inhomogeneous or weighted versions of the local multitype \(K\) and \(L\) functions implemented in localKcross and localLcross.

Given a multitype spatial point pattern X, and two designated types from and to, the local multitype \(K\) function is defined for each point X[i] that belongs to type from, and is computed by $$ K_i(r) = \sqrt{\frac 1 \pi \sum_j \frac{e_{ij}}{\lambda_j}} $$ where the sum is over all points \(j \neq i\) of type to that lie within a distance \(r\) of the \(i\)th point, \(\lambda_j\) is the estimated intensity of the point pattern at the point \(j\), and \(e_{ij}\) is an edge correction term (as described in Kest).

The function \(K_i(r)\) is computed for a range of \(r\) values for each point \(i\). The results are stored as a function value table (object of class "fv") with a column of the table containing the function estimates for each point of the pattern X of type from.

The corresponding \(L\) function \(L_i(r)\) is computed by applying the transformation \(L(r) = \sqrt{K(r)/(2\pi)}\).

See Also

Kinhom, Linhom, localK, localL.

Examples

  X <- amacrine

  # compute all the local L functions
  L <- localLcross.inhom(X)

  # plot all the local L functions against r
  plot(L, main="local L functions for ponderosa", legend=FALSE)

  # plot only the local L function for point number 7
  plot(L, iso007 ~ r)