# Gfox

##### Foxall's Distance Functions

Given a point pattern `X`

and a spatial object `Y`

,
compute estimates of Foxall's $G$ and $J$ functions.

- Keywords
- spatial, nonparametric

##### Usage

```
Gfox(X, Y, r = NULL, breaks = NULL, correction = c("km", "rs", "han"), ...)
Jfox(X, Y, r = NULL, breaks = NULL, correction = c("km", "rs", "han"), ...)
```

##### 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. - 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 conditio
- breaks
- An alternative to the argument
`r`

. Not normally invoked by the user. - 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"`

. - ...
- 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

##### 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 $R$:
$$G(r) = P(R \le r)$$
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
$$H(r) = P(S \le r)$$
which is computed by `Hest`

.

Foxall's $J$-function is the ratio
$$J(r) = \frac{1-G(r)}{1-H(r)}$$
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.

##### 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

##### Examples

```
data(copper)
X <- copper$SouthPoints
Y <- copper$SouthLines
G <- Gfox(X,Y)
J <- Jfox(X,Y, correction="km")
<testonly>J <- Jfox(X,Y, correction="km", eps=1)</testonly>
J <- Jfox(X,Y, correction="km", eps=0.25)
```

*Documentation reproduced from package spatstat, version 1.23-5, License: GPL (>= 2)*