# GmultiInhom

##### Inhomogeneous Marked G-Function

For a marked point pattern, estimate the inhomogeneous version of the multitype \(G\) function, effectively the cumulative distribution function of the distance from a point in subset \(I\) to the nearest point in subset \(J\), adjusted for spatially varying intensity.

- Keywords
- spatial, nonparametric

##### Usage

```
GmultiInhom(X, I, J,
lambda = NULL, lambdaI = NULL, lambdaJ = NULL,
lambdamin = NULL, …,
r = NULL,
ReferenceMeasureMarkSetI = NULL,
ratio = FALSE)
```

##### Arguments

- X
A spatial point pattern (object of class

`"ppp"`

.- I
A subset index specifying the subset of points

*from*which distances are measured. Any kind of subset index acceptable to`[.ppp`

.- J
A subset index specifying the subset of points

*to*which distances are measured. Any kind of subset index acceptable to`[.ppp`

.- lambda
Intensity estimates for each point of

`X`

. A numeric vector of length equal to`npoints(X)`

. Incompatible with`lambdaI,lambdaJ`

.- lambdaI
Intensity estimates for each point of

`X[I]`

. A numeric vector of length equal to`npoints(X[I])`

. Incompatible with`lambda`

.- lambdaJ
Intensity estimates for each point of

`X[J]`

. A numeric vector of length equal to`npoints(X[J])`

. Incompatible with`lambda`

.- lambdamin
A lower bound for the intensity, or at least a lower bound for the values in

`lambdaJ`

or`lambda[J]`

.- …
Ignored.

- r
Vector of distance values at which the inhomogeneous \(G\) function should be estimated. There is a sensible default.

- ReferenceMeasureMarkSetI
Optional. The total measure of the mark set. A positive number.

- ratio
Logical value indicating whether to save ratio information.

##### Details

See Cronie and Van Lieshout (2015).

##### Value

Object of class `"fv"`

containing the estimate of the
inhomogeneous multitype \(G\) function.

##### References

Cronie, O. and Van Lieshout, M.N.M. (2015)
Summary statistics for inhomogeneous marked point processes.
*Annals of the Institute of Statistical Mathematics*
DOI: 10.1007/s10463-015-0515-z

##### See Also

##### Examples

```
# NOT RUN {
X <- rescale(amacrine)
I <- (marks(X) == "on")
J <- (marks(X) == "off")
mod <- ppm(X ~ marks * x)
lam <- fitted(mod, dataonly=TRUE)
lmin <- min(predict(mod)[["off"]]) * 0.9
plot(GmultiInhom(X, I, J, lambda=lam, lambdamin=lmin))
# equivalent
plot(GmultiInhom(X, I, J, lambdaI=lam[I], lambdaJ=lam[J], lambdamin=lmin),
main="")
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*