Simulation Envelopes of Summary Function for 3D Point Pattern
Computes simulation envelopes of a summary function for a three-dimensional point pattern.
## S3 method for class 'pp3': envelope(Y, fun=K3est, 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, maxnerr=nsim)
- A three-dimensional point pattern (object of class
- Function that computes the desired summary statistic for a 3D point pattern.
- Number of simulated point patterns to be generated when computing the envelopes.
- Integer. Rank of the envelope value amongst the
nsimsimulated values. A rank of 1 means that the minimum and maximum simulated values will be used.
- Extra arguments passed to
- Optional. Specifies how to generate the simulated point patterns.
simulateis an expression in the R language, then this expression will be evaluated
nsimtimes, to obtain
nsimpoint patterns which are
- Logical flag indicating whether to print progress reports during the simulations.
- Optional. A transformation to be applied to the function values, before the envelopes are computed. An expression object (see Details).
- Logical flag indicating whether envelopes should be pointwise
global=FALSE) or simultaneous (
A vector of length 2 specifying
the interval of $r$ values for the simultaneous critical
envelopes. Only relevant if
- Logical flag indicating whether to save all the simulated function values.
- Logical flag indicating whether to save all the simulated point patterns.
- 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=TRUEand the simulations are not based on CSR.
- Logical. If
TRUE, critical envelopes will be calculated as sample mean plus or minus
nSDtimes sample standard deviation.
- Number of estimated standard deviations used to determine
the critical envelopes, if
- Character string that should be used as the name of the
data point pattern
Ywhen printing or plotting the results.
- Maximum number of rejected patterns.
funyields an error when applied to a simulated point pattern (for example, because the pattern is empty and
funrequires at least one point), the pattern will be rejected a
envelope command performs simulations and
computes envelopes of a summary statistic based on the simulations.
The result is an object that can be plotted to display the envelopes.
The envelopes can be used to assess the goodness-of-fit of
a point process model to point pattern data.
envelope function is generic, with methods for
described in the help file for
envelope.pp3 is the method for
three-dimensional point patterns (objects of class
For the most basic use, if you have a 3D point pattern
you want to test Complete Spatial Randomness (CSR), type
plot(envelope(X, K3est,nsim=39)) to see the three-dimensional
$K$ function for
X plotted together with the envelopes of
the three-dimensional $K$ function for 39 simulations of CSR.
To create simulation envelopes, the command
nsim random point patterns
in one of the following ways.
simulate=NULL, then we generate
nsimsimulations of Complete Spatial Randomness (i.e.
nsimsimulated point patterns each being a realisation of the uniform Poisson point process) with the same intensity as the pattern
simulateis supplied, then it determines how the simulated point patterns are generated. See
funis applied to each of these simulated patterns. Typically
funis one of the functions
pcf3est. It may also be a character string containing the name of one of these functions. For further information, see the documentation for
- A function value table (object of class
"fv") which can be plotted directly. See
envelopefor further details.
Baddeley, A.J, Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42, 641--668.
X <- rpoispp3(20, box3()) plot(envelope(X, nsim=39)) <testonly>plot(envelope(X, nsim=4))</testonly>