# Poisson

From spatstat v1.18-1
by Adrian Baddeley

##### Poisson Point Process Model

Creates an instance of the Poisson point process model which can then be fitted to point pattern data.

##### Usage

`Poisson()`

##### Details

The function `ppm`

, which fits point process models to
point pattern data, requires an argument `interaction`

of class `"interact"`

describing the interpoint interaction structure
of the model to be fitted.
The appropriate description of the Poisson process is
provided by the value of the function `Poisson`

.

This works for all types of Poisson processes including multitype and nonstationary Poisson processes.

##### Value

- An object of class
`"interact"`

describing the interpoint interaction structure of the Poisson point process (namely, there are no interactions).

##### See Also

##### Examples

```
data(nztrees)
ppm(nztrees, ~1, Poisson())
# fit the stationary Poisson process to 'nztrees'
# no edge correction needed
data(longleaf)
<testonly>longleaf <- longleaf[seq(1, longleaf$n, by=50)]</testonly>
longadult <- longleaf[longleaf$marks >= 30, ]
longadult <- unmark(longadult)
ppm(longadult, ~ x, Poisson())
# fit the nonstationary Poisson process
# with intensity lambda(x,y) = exp( a + bx)
data(lansing)
# trees marked by species
<testonly>lansing <- lansing[seq(1,lansing$n, by=30), ]</testonly>
ppm(lansing, ~ marks, Poisson())
# fit stationary marked Poisson process
# with different intensity for each species
ppm(lansing, ~ marks * polynom(x,y,3), Poisson())
# fit nonstationary marked Poisson process
# with different log-cubic trend for each species
<testonly># equivalent functionality - smaller dataset
data(betacells)
ppm(betacells, ~ marks * polynom(x,y,2), Poisson())</testonly>
```

*Documentation reproduced from package spatstat, version 1.18-1, License: GPL (>= 2)*

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