splancs (version 2.01-45)

Fzero: Theoretical nearest neighbour distribution function

Description

Calculate the theoretical nearest neighbour distribution function.

Usage

Fzero(density,s)

Value

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

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)).

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.

See Also

Fhat,Ghat,pdense

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)