# rLGCP

##### Simulate Log-Gaussian Cox Process

Generate a random point pattern, a realisation of the log-Gaussian Cox process.

##### Usage

```
rLGCP(model="exp", mu = 0, param = NULL,
…,
win=NULL, saveLambda=TRUE, nsim=1, drop=TRUE)
```

##### Arguments

- model
character string: the short name of a covariance model for the Gaussian random field. After adding the prefix

`"RM"`

, the code will search for a function of this name in the RandomFields package.- mu
mean function of the Gaussian random field. Either a single number, a

`function(x,y, ...)`

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

).- param
List of parameters for the covariance. Standard arguments are

`var`

and`scale`

.- …
Additional parameters for the covariance, or arguments passed to

`as.mask`

to determine the pixel resolution.- win
Window in which to simulate the pattern. An object of class

`"owin"`

.- saveLambda
Logical. If

`TRUE`

(the default) then the simulated random intensity will also be saved, and returns as an attribute of the point pattern.- nsim
Number of simulated realisations to be generated.

- drop
Logical. If

`nsim=1`

and`drop=TRUE`

(the default), the result will be a point pattern, rather than a list containing a point pattern.

##### Details

This function generates a realisation of a log-Gaussian Cox process (LGCP). This is a Cox point process in which the logarithm of the random intensity is a Gaussian random field with mean function \(\mu\) and covariance function \(c(r)\). Conditional on the random intensity, the point process is a Poisson process with this intensity.

The string `model`

specifies the covariance
function of the Gaussian random field, and the parameters
of the covariance are determined by `param`

and `…`

.

To determine the covariance model, the string `model`

is prefixed by `"RM"`

, and a function of this name is
sought in the RandomFields package.
For a list of available models see
`RMmodel`

in the
RandomFields package. For example the
Matern covariance is specified by `model="matern"`

, corresponding
to the function `RMmatern`

in the RandomFields package.

Standard variance parameters (for all functions beginning with
`"RM"`

in the RandomFields package) are `var`

for the variance at distance zero, and `scale`

for the scale
parameter. Other parameters are specified in the help files
for the individual functions beginning with `"RM"`

. For example
the help file for `RMmatern`

states that `nu`

is a parameter
for this model.

This algorithm uses the function `RFsimulate`

in the
RandomFields package to generate values of
a Gaussian random field, with the specified mean function `mu`

and the covariance specified by the arguments `model`

and
`param`

, on the points of a regular grid. The exponential
of this random field is taken as the intensity of a Poisson point
process, and a realisation of the Poisson process is then generated by the
function `rpoispp`

in the spatstat package.

If the simulation window `win`

is missing or `NULL`

,
then it defaults to
`Window(mu)`

if `mu`

is a pixel image,
and it defaults to the unit square otherwise.

The LGCP model can be fitted to data using `kppm`

.

##### Value

A point pattern (object of class `"ppp"`

)
or a list of point patterns.

Additionally, the simulated intensity function for each point pattern is
returned as an attribute `"Lambda"`

of the point pattern,
if `saveLambda=TRUE`

.

##### References

Moller, J., Syversveen, A. and Waagepetersen, R. (1998)
Log Gaussian Cox Processes.
*Scandinavian Journal of Statistics* **25**, 451--482.

##### See Also

`rpoispp`

,
`rMatClust`

,
`rGaussPoisson`

,
`rNeymanScott`

,
`lgcp.estK`

,
`kppm`

##### Examples

```
# NOT RUN {
if(require(RandomFields)) {
# homogeneous LGCP with exponential covariance function
X <- rLGCP("exp", 3, var=0.2, scale=.1)
# inhomogeneous LGCP with Gaussian covariance function
m <- as.im(function(x, y){5 - 1.5 * (x - 0.5)^2 + 2 * (y - 0.5)^2}, W=owin())
X <- rLGCP("gauss", m, var=0.15, scale =0.5)
plot(attr(X, "Lambda"))
points(X)
# inhomogeneous LGCP with Matern covariance function
X <- rLGCP("matern", function(x, y){ 1 - 0.4 * x},
var=2, scale=0.7, nu=0.5,
win = owin(c(0, 10), c(0, 10)))
plot(X)
}
# }
```

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