Lhat function

Estimation of the L function

Estimates the L function

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: $L(r)=\sqrt{\frac{K}{\pi}}-r$.

Returns

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.

See Also

Khat, LEnvelope

Examples

data(paracou16)
autoplot(paracou16)

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

# Plot
autoplot(Paracou)