# linearKinhom

##### Inhomogeneous Linear K Function

Computes an estimate of the inhomogeneous linear $K$ function for a point pattern on a linear network.

- Keywords
- spatial, nonparametric

##### Usage

`linearKinhom(X, lambda=NULL, r=NULL, ..., correction="Ang", normalise=TRUE)`

##### Arguments

- X
- Point pattern on linear network (object of class
`"lpp"`

). - lambda
- Intensity values for the point pattern. Either a numeric vector,
a
`function`

, a pixel image (object of class`"im"`

or`"linim"`

) or a fitted point process model (object of class`"ppm"`

or - r
- Optional. Numeric vector of values of the function argument $r$. There is a sensible default.
- ...
- Ignored.
- correction
- Geometry correction.
Either
`"none"`

or`"Ang"`

. See Details. - normalise
- Logical. If
`TRUE`

(the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the data points), which reduces the sampling variability. If`FALSE`

, the denominato

##### Details

This command computes the inhomogeneous version of the linear $K$ function from point pattern data on a linear network.

If `lambda = NULL`

the result is equivalent to the
homogeneous $K$ function `linearK`

.
If `lambda`

is given, then it is expected to provide estimated values
of the intensity of the point process at each point of `X`

.
The argument `lambda`

may be a numeric vector (of length equal to
the number of points in `X`

), or a `function(x,y)`

that will be
evaluated at the points of `X`

to yield numeric values,
or a pixel image (object of class `"im"`

) or a fitted point
process model (object of class `"ppm"`

or `"lppm"`

).

If `lambda`

is a fitted point process model,
the default behaviour is to update the model by re-fitting it to
the data, before computing the fitted intensity.
This can be disabled by setting `update=FALSE`

.
If `correction="none"`

, the calculations do not include
any correction for the geometry of the linear network.
If `correction="Ang"`

, the pair counts are weighted using
Ang's correction (Ang, 2010).

##### Value

- Function value table (object of class
`"fv"`

).

##### References

Ang, Q.W. (2010) Statistical methodology for spatial point patterns
on a linear network. MSc thesis, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012)
Geometrically corrected second-order analysis of
events on a linear network, with applications to
ecology and criminology.
*Scandinavian Journal of Statistics* **39**, 591--617.

##### See Also

##### Examples

```
data(simplenet)
X <- rpoislpp(5, simplenet)
fit <- lppm(X, ~x)
K <- linearKinhom(X, lambda=fit)
plot(K)
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*