R: Envelope of K12hat from random toroidal shifts of two point...

Kenv.tor {splancs} | R Documentation

## Envelope of K12hat from random toroidal shifts of two point patterns

### Description

Compute envelope of K12hat from random toroidal shifts of two point patterns.

### Usage

    Kenv.tor(pts1,pts2,poly,nsim,s,quiet=FALSE)

### Arguments

`pts1` | First point data set.
`pts2` | Second point data set.
`poly` | Polygon containing the points.
`nsim` | Number of random toroidal shifts to do.
`s` | Vector of distances at which to calculate the envelope.
`quiet` | If FALSE, print a message after every simulation for progress monitoring. If true, print no messages.

### Details

The second point data set is randomly shifted using `rtor.shift` in the rectangle defined by `poly`. Then `k12hat` is called to compute K12hat for the two patterns. The upper and lower values of K12hat over the `ntor` toroidal shifts are returned.

### Value

A list with two components, called `$upper` and `$lower`. Each component is a vector like `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: 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

`rtor.shift`,`k12hat`

### Examples

    data(okwhite)
    data(okblack)
    okpoly <- list(x=c(okwhite$x, okblack$x), y=c(okwhite$y, okblack$y))
    plot(seq(5,80,5), sqrt(k12hat(as.points(okwhite), as.points(okblack),
    bboxx(bbox(as.points(okpoly))), seq(5,80,5))/pi) - seq(5,80,5), xlab="distance",
    ylab=expression(hat(L)[12]), ylim=c(-35,35), type="l",
    main="Simulation envelopes, random toroidal shifts")
    env.ok <- Kenv.tor(as.points(okwhite), as.points(okblack),
    bboxx(bbox(as.points(okpoly))), nsim=29, s=seq(5,80,5))
    lines(seq(5,80,5), sqrt(env.ok$upper/pi)-seq(5,80,5), lty=2)
    lines(seq(5,80,5), sqrt(env.ok$lower/pi)-seq(5,80,5), lty=2)

[Package splancs version 2.01-43 Index]