Estimation of the L function

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.

References

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

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.

Examples

data(paracou16)
autoplot(paracou16)


# Calculate L
r <- 0:30
(Paracou <- Lhat(paracou16, r))
#> Function value object (class ‘fv’)
#> for the function r -> L(r)
#> ................................................................
#>      Math.label     Description                                 
#> r    r              distance argument r                         
#> theo L[pois](r)     theoretical Poisson L(r)                    
#> iso  hat(L)[iso](r) Ripley isotropic correction estimate of L(r)
#> ................................................................
#> Default plot formula:  .~r
#> where “.” stands for ‘iso’, ‘theo’
#> Recommended range of argument r: [0, 30]
#> Available range of argument r: [0, 30]
#> Unit of length: 1 meter

# Plot
autoplot(Paracou)