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 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"
. Alternativelycorrection="all"
selects all options.- …
Extra arguments affecting the discretisation of distances. These arguments are ignored by
Gfox
, butJfox
passes them toHest
to determine the discretisation of the spatial domain.
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
# NOT RUN {
data(copper)
X <- copper$SouthPoints
Y <- copper$SouthLines
G <- Gfox(X,Y)
J <- Jfox(X,Y, correction="km")
# }
# NOT RUN {
# }
# NOT RUN {
J <- Jfox(X,Y, correction="km", eps=0.25)
# }