# 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.

Keywords
spatial, nonparametric
##### 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

r

the values of the argument $$r$$ at which the function $$L_{i\bullet}(r)$$ has been estimated

theo

the 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)Li.(r) obtained by the edge corrections named.

The argument i is interpreted as a level of the factor X$marks. It is converted to a character string if it is not already a character string. The value i=1 does not refer to the first level of the factor. ##### References Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003. ##### See Also Ldot, Linhom, Kdot.inhom, Lcross.inhom. ##### Aliases • Ldot.inhom ##### Examples # NOT RUN { # Lansing Woods data lan <- lansing lan <- lan[seq(1,npoints(lan), by=10)] ma <- split(lan)$maple
lg <- unmark(lan)

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

# 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)
# }

Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)

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