R: Theoretical nearest neighbour distribution function

Fzero {splancs} | R Documentation

## Theoretical nearest neighbour distribution function

### Description

Calculate the theoretical nearest neighbour distribution function.

### Usage

    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

### 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))`.

### Value

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

### 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: http://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)

[Package splancs version 2.01-40 Index]