Estimation of the Lmm function

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.

Details

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

Value

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

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.

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))
#> Function value object (class ‘fv’)
#> for the function r -> L[mm](r)
#> .............................................................................
#>      Math.label              Description                                     
#> r    r                       distance argument r                             
#> theo {L[mm][]^{pois}}(r)     theoretical Poisson L[mm](r)                    
#> iso  {hat(L[mm])[]^{iso}}(r) Ripley isotropic correction estimate of L[mm](r)
#> .............................................................................
#> Default plot formula:  .~.x
#> where “.” stands for ‘iso’, ‘theo’
#> Recommended range of argument r: [0, 50]
#> Available range of argument r: [0, 50]
#> Unit of length: 1 meter

# Plot
autoplot(Paracou)