Inhomogeneous Multitype L Dot Function
For a multitype point pattern, estimate the inhomogeneous version of the dot L function.
Ldot.inhom(X, i, ..., correction)
X |
The observed point pattern, from which an estimate of the inhomogeneous cross type L function Li.(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 |
correction,... |
Other arguments passed to |
All the arguments are passed to Kdot.inhom, which
estimates the inhomogeneous multitype K function
Ki.(r) for the point pattern.
The resulting values are then
transformed by taking L(r) = sqrt(K(r)/pi).
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 Li.(r) has been estimated |
theo |
the theoretical value of Li.(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 Li.(r)
obtained by the edge corrections named.
The argument i is interpreted as
a level of the factor X$marks. It is converted to a character
string if it is not already a character string.
The value i=1 does not
refer to the first level of the factor.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
# Lansing Woods data
lan <- lansing
lan <- lan[seq(1,npoints(lan), by=10)]
ma <- split(lan)$maple
lg <- unmark(lan)
# Estimate intensities by nonparametric smoothing
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdadot <- density.ppp(lg, sigma=0.15, at="points")
L <- Ldot.inhom(lan, "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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.