# is.stationary

##### Recognise Stationary and Poisson Point Process Models

Given a point process model that has been fitted to data, determine whether the model is a stationary point process, and whether it is a Poisson point process.

##### Usage

```
is.stationary(x)
# S3 method for ppm
is.stationary(x)
# S3 method for kppm
is.stationary(x)
# S3 method for lppm
is.stationary(x)
# S3 method for slrm
is.stationary(x)
# S3 method for rmhmodel
is.stationary(x)
# S3 method for dppm
is.stationary(x)
# S3 method for detpointprocfamily
is.stationary(x)
```is.poisson(x)
# S3 method for ppm
is.poisson(x)
# S3 method for kppm
is.poisson(x)
# S3 method for lppm
is.poisson(x)
# S3 method for slrm
is.poisson(x)
# S3 method for rmhmodel
is.poisson(x)
# S3 method for interact
is.poisson(x)

##### Arguments

- x
A fitted spatial point process model (object of class

`"ppm"`

,`"kppm"`

,`"lppm"`

,`"dppm"`

or`"slrm"`

) or similar object.

##### Details

The argument `x`

represents a fitted spatial point process model
or a similar object.

`is.stationary(x)`

returns `TRUE`

if `x`

represents
a stationary point process, and `FALSE`

if not.

`is.poisson(x)`

returns `TRUE`

if `x`

represents
a Poisson point process, and `FALSE`

if not.

The functions `is.stationary`

and `is.poisson`

are generic,
with methods for the classes `"ppm"`

(Gibbs point process models),
`"kppm"`

(cluster or Cox point process models),
`"slrm"`

(spatial logistic regression models) and
`"rmhmodel"`

(model specifications for the
Metropolis-Hastings algorithm).
Additionally `is.stationary`

has a method for
classes `"detpointprocfamily"`

and `"dppm"`

(both determinantal point processes) and
`is.poisson`

has a method for
class `"interact"`

(interaction structures for Gibbs models).

`is.poisson.kppm`

will return `FALSE`

, unless
the model `x`

is degenerate:
either `x`

has zero intensity so that its realisations are empty
with probability 1, or it is a log-Gaussian Cox process
where the log intensity has zero variance.

`is.poisson.slrm`

will always return `TRUE`

,
by convention.

##### Value

A logical value.

##### See Also

`is.marked`

to determine whether a model is a marked
point process.

`summary.ppm`

for detailed information.

##### Examples

```
# NOT RUN {
data(cells)
data(redwood)
fit <- ppm(cells ~ x)
is.stationary(fit)
is.poisson(fit)
fut <- kppm(redwood ~ 1, "MatClust")
is.stationary(fut)
is.poisson(fut)
fot <- slrm(cells ~ x)
is.stationary(fot)
is.poisson(fot)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*