# Lmmhat: Estimation of the Lmm function In dbmss: Distance-Based Measures of Spatial Structures

## Description

Estimates the Lmm function

## Usage

 1 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)=√{\frac{Kmm}{π}}-r.

## Value

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

## Author(s)

Eric Marcon <[email protected]>

## 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.

Kmmhat, LmmEnvelope
  1 2 3 4 5 6 7 8 9 10 11 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)