Theoretical nearest neighbour distribution function

Calculate the theoretical nearest neighbour distribution function.

Fzero(density,s)

Arguments

density

The density of the point pattern, i.e. the number of points per unit area.

s

A vector of distances at which to evaluate Fzero

Value

A vector of the same length as s, containing the value of Fzero at the distances in s.

Details

Fzero returns the nearest neighbour distribution for a homogeneous planar Poisson process. In fortran notation, Fzero(s) is FZERO = 1-EXP(-PI*DENSITY*(S**2)).

See also

Fhat,Ghat,pdense

References

Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.

Examples

data(uganda)
plot(Ghat(as.points(uganda), seq(20, 500, 20)), Fzero(pdense(as.points(uganda), 
uganda$poly), seq(20, 500, 20)), type="l", ylab="Theoretical G", 
xlab="Estimated G")
lines(c(0,1),c(0,1),lty=2)