Simulation envelopes can be used to assess the goodness-of-fit of
a point process model to point pattern data. See the References. If Y
is a point pattern (an object of class "ppp"
)
then this routine generates nsim
simulations of
Complete Spatial Randomness (i.e. nsim
simulated point patterns
each being a realisation of the uniform Poisson point process)
with the same intensity as the pattern Y
.
If Y
is a fitted point process model (an object of class
"ppm"
) then this routine generates nsim
simulated
realisations of that model.
The summary statistic fun
is applied to each of these simulated
patterns. Typically fun
is one of the functions
Kest
, Gest
, Fest
, Jest
or pcf
.
It can also be a home-made function; it should return an object
of class "fv"
.
Upper and lower pointwise envelopes are computed pointwise (i.e.
for each value of the distance argument $r$), by sorting the
nsim
simulated values, and taking the m
-th lowest
and m
-th highest values, where m = nrank
.
For example if nrank=1
, the upper and lower envelopes
are the pointwise maximum and minimum of the simulated values.
The significance level of the associated Monte Carlo test is
alpha = 2 * nrank/(1 + nsim)
.
The return value is an object of class "fv"
containing
the summary function for the data point pattern
and the upper and lower simulation envelopes. It can be plotted
using plot.fv
.
Arguments can be passed to the function fun
through
...
. This makes it possible to select the edge correction
used to calculate the summary statistic. See the Examples.