Lhat: Estimation of the L function

In dbmss: Distance-Based Measures of Spatial Structures

Estimation of the L function

Description

Estimates the L function

Usage

Lhat(X, r = NULL, ReferenceType = "", NeighborType = "", 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. Default is all point types.
NeighborType	One of the point types. 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

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

Value

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

Note

L was originally defined as L(r)=\sqrt{\frac{K}{\pi}}. It has been used as L(r)=\sqrt{\frac{K}{\pi}}-r in a part of the literature because this normalization is easier to plot.

References

Besag, J. E. (1977). Comments on Ripley's paper. Journal of the Royal Statistical Society B 39(2): 193-195.

See Also

Khat, LEnvelope

Examples

data(paracou16)
autoplot(paracou16)

# Calculate L
r <- 0:30
(Paracou <- Lhat(paracou16, r))

# Plot
autoplot(Paracou)

dbmss documentation built on June 8, 2025, 1:59 p.m.