Estimation of the K function

Estimates the K function

Usage

Khat(X, r = NULL, ReferenceType = "", NeighborType = 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. Default is all point types.
NeighborType: One of the point types. By default, the same as reference type.
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

K is a cumulative, topographic measure of a point pattern structure.

Value

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

References

Ripley, B. D. (1976). The Foundations of Stochastic Geometry. Annals of Probability 4(6): 995-998.

Ripley, B. D. (1977). Modelling Spatial Patterns. Journal of the Royal Statistical Society B 39(2): 172-212.

Note

The computation of Khat relies on spatstat functions Kest and Kcross.

Examples

data(paracou16)
autoplot(paracou16)


# Calculate K
r <- 0:30
(Paracou <- Khat(paracou16, r))
#> Function value object (class ‘fv’)
#> for the function r -> K(r)
#> ................................................................
#>      Math.label     Description                                 
#> r    r              distance argument r                         
#> theo K[pois](r)     theoretical Poisson K(r)                    
#> iso  hat(K)[iso](r) Ripley isotropic correction estimate of K(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 (after normalization by pi.r^2)
autoplot(Paracou, ./(pi*r^2) ~ r)