# rLGCP

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##### Simulate Log-Gaussian Cox Process

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

##### Usage
rLGCP(model="exponential", mu = 0, param = NULL, ..., win=NULL)
##### Arguments
model
character string: the name of a covariance model for the Gaussian random field, as recognised by the function GaussRF 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
Numeric vector of parameters for the covariance, as understood by the function GaussRF in the RandomFields package.
...
Further arguments passed to the function GaussRF in the RandomFields package.
win
Window in which to simulate the pattern. An object of class "owin".
##### 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 arguments model and param specify the covariance function of the Gaussian random field, in the format expected by the RandomFields package. See GaussRF or Covariance for information about this format. A list of all implemented models is available by typing PrintModelList(). This algorithm uses the function GaussRF 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 as.owin(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

• The simulated point pattern (an object of class "ppp").

Additionally, the simulated intensity function is returned as an attribute "Lambda".

##### References

latex{Mller{Moller}, J., Syversveen, A. and Waagepetersen, R. (1998) Log Gaussian Cox Processes. Scandinavian Journal of Statistics 25, 451--482. } if(require(RandomFields)) { # homogeneous LGCP with exponential covariance function X <- rLGCP("exp", 3, c(0, variance=0.2, nugget=0, 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, c(0, variance=0.15, nugget = 0, 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}, c(0, variance=2, nugget=0, scale=0.7, a = 0.5), win = owin(c(0, 10), c(0, 10))) plot(X) } else message("Simulation requires the RandomFields package")

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##### See Also

rpoispp, rMatClust, rGaussPoisson, rNeymanScott, lgcp.estK, kppm

##### Aliases
• rLGCP
Documentation reproduced from package spatstat, version 1.36-0, License: GPL (>= 2)

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