dbmss (version 2.9-2)

Lmmhat: Estimation of the Lmm function

Description

Estimates the Lmm function

Usage

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

Value

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

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.

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))
autoplot(X, 
  labelSize = expression("Basal area (" ~cm^2~ ")"), 
  labelColor = "Species")

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

# Plot
autoplot(Paracou)