dbmss (version 2.1.2)

Lmmhat: Estimation of the Lmm function

Description

Estimates the Lmm function

Usage

Lmmhat(X, r = NULL, ReferenceType = "", CheckArguments = TRUE)

Arguments

X

A weighted, marked, planar point pattern (wmppp.object).

r

A vector of distances. If NULL, a sensible default value is chosen (512 intervals, from 0 to half the diameter of the window) following spatstat.

ReferenceType

One of the point types. Others are ignored. Default is all point types.

CheckArguments

Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.

Value

• An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Details

Lmm is the normalized version of Kmm: $Lmm(r)=\sqrt{\frac{Kmm}{\pi}}-r$.

References

Penttinen, A., Stoyan, D. and Henttonen, H. M. (1992). Marked Point Processes in Forest Statistics. Forest Science 38(4): 806-824. Espa, G., Giuliani, D. and Arbia, G. (2010). Weighting Ripley's K-function to account for the firm dimension in the analysis of spatial concentration. Discussion Papers, 12/2010. Universita di Trento, Trento: 26.

See Also

Kmmhat, LmmEnvelope

Examples

data(paracou16)
# Keep only 50\% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.5))
plot(X)

# Calculate Lmm
r <- seq(0, 30, 2)
(Paracou <- Lmmhat(X, r))

# Plot
plot(Paracou)