# Ldot.inhom

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##### Inhomogeneous Multitype L Dot Function

For a multitype point pattern, estimate the inhomogeneous version of the dot $L$ function.

##### Usage
Ldot.inhom(X, i, ...)
##### Arguments
X
The observed point pattern, from which an estimate of the inhomogeneous cross type $L$ function $L_{i\bullet}(r)$ will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
i
The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).
...
Other arguments passed to Kdot.inhom.
##### Details

This a generalisation of the function Ldot to include an adjustment for spatially inhomogeneous intensity, in a manner similar to the function Linhom.

All the arguments are passed to Kdot.inhom, which estimates the inhomogeneous multitype K function $K_{i\bullet}(r)$ for the point pattern. The resulting values are then transformed by taking $L(r) = \sqrt{K(r)/\pi}$.

##### Value

• An object of class "fv" (see fv.object).

Essentially a data frame containing numeric columns

• rthe values of the argument $r$ at which the function $L_{i\bullet}(r)$ has been estimated
• theothe theoretical value of $L_{i\bullet}(r)$ for a marked Poisson process, identical to $r$.
• 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 $L_{i\bullet}(r)$ obtained by the edge corrections named.

##### References

latex{Mller{Moller}, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003. }

Warnings
{ The argument i is interpreted as a level of the factor X$marks. It is converted to a character string if it is not already a character string. The value i=1 does not refer to the first level of the factor. } Ldot, Linhom, Kdot.inhom, Lcross.inhom. # Lansing Woods data data(lansing) lansing <- lansing[seq(1,lansing$n, by=10)] ma <- split(lansing)\$maple lg <- unmark(lansing)

# Estimate intensities by nonparametric smoothing lambdaM <- density.ppp(ma, sigma=0.15, at="points") lambdadot <- density.ppp(lg, sigma=0.15, at="points") L <- Ldot.inhom(lansing, "maple", lambdaI=lambdaM, lambdadot=lambdadot)

# synthetic example: type A points have intensity 50, # type B points have intensity 50 + 100 * x lamB <- as.im(function(x,y){50 + 100 * x}, owin()) lamdot <- as.im(function(x,y) { 100 + 100 * x}, owin()) X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB)) L <- Ldot.inhom(X, "B", lambdaI=lamB, lambdadot=lamdot)

[object Object],[object Object],[object Object] spatial nonparametric

##### Aliases
• Ldot.inhom
Documentation reproduced from package spatstat, version 1.36-0, License: GPL (>= 2)

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