R: Foxall's Distance Functions

Gfox {spatstat.core} | R Documentation

## Foxall's Distance Functions

### Description

Given a point pattern `X` and a spatial object `Y`, compute estimates of Foxall's G and J functions.

### Usage

    Gfox(X, Y, r=NULL, breaks=NULL, correction=c("km", "rs", "han"), W, ...)
    Jfox(X, Y, r=NULL, breaks=NULL, correction=c("km", "rs", "han"), W, ...,
         warn.trim=TRUE)

### Arguments

`X` | A point pattern (object of class `"ppp"`) from which distances will be measured.
`Y` | An object of class `"ppp"`, `"psp"` or `"owin"` to which distances will be measured. Alternatively a pixel image (class `"im"`) with logical values.
`r` | Optional. Numeric vector. The values of the argument r at which Gfox(r) or Jfox(r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r.
`breaks` | This argument is for internal use only.
`correction` | Optional. The edge correction(s) to be used to estimate Gfox(r) or Jfox(r). A vector of character strings selected from `"none"`, `"rs"`, `"km"`, `"cs"` and `"best"`. Alternatively `correction="all"` selects all options.
`W` | Optional. A window (object of class `"owin"`) to be taken as the window of observation. The distribution function will be estimated from data inside `W`. The default is `W=Frame(Y)` when `Y` is a window, and `W=Window(Y)` otherwise.
`...` | Extra arguments affecting the discretisation of distances. These arguments are ignored by `Gfox`, but `Jfox` passes them to `Hest` to determine the discretisation of the spatial domain.
`warn.trim` | Logical value indicating whether a warning should be issued by `Jfox` when the window of `X` had to be trimmed in order to be a subset of the frame of `Y`.

### Details

Given a point pattern `X` and another spatial object `Y`, these functions compute two nonparametric measures of association between `X` and `Y`, introduced by Foxall (Foxall and Baddeley, 2002).

Let the random variable R be the distance from a typical point of `X` to the object `Y`. Foxall's G-function is the cumulative distribution function of R:

P(R <= r)

Let the random variable S be the distance from a fixed point in space to the object `Y`. The cumulative distribution function of S is the (unconditional) spherical contact distribution function

H(r) = P(S <= r)

which is computed by `Hest`.

Foxall's J-function is the ratio

J(r) = (1-G(r))/(1-H(r))

For further interpretation, see Foxall and Baddeley (2002).

Accuracy of `Jfox` depends on the pixel resolution, which is controlled by the arguments `eps`, `dimyx` and `xy` passed to `as.mask`. For example, use `eps=0.1` to specify square pixels of side 0.1 units, and `dimyx=256` to specify a 256 by 256 grid of pixels.

### Value

A function value table (object of class `"fv"`) which can be printed, plotted, or converted to a data frame of values.

### Author(s)

Rob Foxall and Adrian Baddeley Adrian.Baddeley@curtin.edu.au

### References

Foxall, R. and Baddeley, A. (2002) Nonparametric measures of association between a spatial point process and a random set, with geological applications. Applied Statistics 51, 165–182.

### See Also

`Gest`, `Hest`, `Jest`, `Fest`

### Examples

      data(copper)
      X <- copper$SouthPoints
      Y <- copper$SouthLines
      G <- Gfox(X,Y)
      J <- Jfox(X,Y, correction="km")

[Package spatstat.core version 2.4-4 Index]