# envelope.lpp

##### Envelope for Point Patterns on Linear Network

Enables envelopes to be computed for point patterns on a linear network.

- Keywords
- spatial

##### Usage

```
## S3 method for class 'lpp':
envelope(Y, fun=linearK, nsim=99, nrank=1, \dots,
simulate=NULL, verbose=TRUE,
transform=NULL,global=FALSE,ginterval=NULL,
savefuns=FALSE, savepatterns=FALSE,
nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL)
## S3 method for class 'lppm':
envelope(Y, fun=linearK, nsim=99, nrank=1, \dots,
simulate=NULL, verbose=TRUE,
transform=NULL,global=FALSE,ginterval=NULL,
savefuns=FALSE, savepatterns=FALSE,
nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL)
```

##### Arguments

- Y
- A point pattern on a linear network
(object of class
`"lpp"`

) or a fitted point process model on a linear network (object of class`"lppm"`

). - fun
- Function that is to be computed for each simulated pattern.
- nsim
- Number of simulations to perform.
- nrank
- Integer. Rank of the envelope value amongst the
`nsim`

simulated values. A rank of 1 means that the minimum and maximum simulated values will be used. - ...
- Extra arguments passed to
`fun`

. - simulate
- Optional. Specifies how to generate the simulated point patterns.
If
`simulate`

is an expression in the R language, then this expression will be evaluated`nsim`

times, to obtain`nsim`

point patterns which are - verbose
- Logical flag indicating whether to print progress reports during the simulations.
- transform
- Optional. A transformation to be applied to the function values, before the envelopes are computed. An expression object (see Details).
- global
- Logical flag indicating whether envelopes should be pointwise
(
`global=FALSE`

) or simultaneous (`global=TRUE`

). - ginterval
- Optional.
A vector of length 2 specifying
the interval of $r$ values for the simultaneous critical
envelopes. Only relevant if
`global=TRUE`

. - savefuns
- Logical flag indicating whether to save all the simulated function values.
- savepatterns
- Logical flag indicating whether to save all the simulated point patterns.
- nsim2
- Number of extra simulated point patterns to be generated
if it is necessary to use simulation to estimate the theoretical
mean of the summary function. Only relevant when
`global=TRUE`

and the simulations are not based on CSR. - VARIANCE
- Logical. If
`TRUE`

, critical envelopes will be calculated as sample mean plus or minus`nSD`

times sample standard deviation. - nSD
- Number of estimated standard deviations used to determine
the critical envelopes, if
`VARIANCE=TRUE`

. - Yname
- Character string that should be used as the name of the
data point pattern
`Y`

when printing or plotting the results.

##### Details

This is a method for the generic
function `envelope`

applicable to point patterns on a linear network.
The argument `Y`

can be either a point pattern on a linear
network, or a fitted point process model on a linear network.
The function `fun`

will be evaluated for the data
and also for `nsim`

simulated point
patterns on the same linear network.
The upper and lower
envelopes of these evaluated functions will be computed
as described in `envelope`

.
The type of simulation is determined as follows.

- if
`Y`

is a point pattern (object of class`"lpp"`

) and`simulate`

is missing or`NULL`

, then random point patterns will be generated according to a Poisson point process on the linear network on which`Y`

is defined, with intensity estimated from`Y`

. - if
`Y`

is a fitted point process model (object of class`"lppm"`

) and`simulate`

is missing or`NULL`

, then random point patterns will be generated by simulating from the fitted model. - If
`simulate`

is present, it should be an expression that can be evaluated to yield random point patterns on the same linear network as`Y`

.

`fun`

should accept as its first argument
a point pattern on a linear network (object of class `"lpp"`

)
and should have another argument called `r`

or a `...`

argument.
##### Value

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

) with additional information, as described in`envelope`

.

##### References

Ang, Q.W. (2010)
*Statistical methodology for events on a network*.
Master's thesis, School of Mathematics and Statistics, 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.
To appear in *Scandinavian Journal of Statistics*.
Okabe, A. and Yamada, I. (2001) The K-function method on a network and
its computational implementation. *Geographical Analysis*
**33**, 271-290.

##### See Also

##### Examples

```
example(lpp)
# uniform Poisson
envelope(X, nsim=4)
# nonuniform Poisson
fit <- lppm(X, ~x)
envelope(fit, nsim=4)
```

*Documentation reproduced from package spatstat, version 1.28-1, License: GPL (>= 2)*