hopskel(X)hopskel.test(X, ...,
alternative=c("two.sided", "less", "greater",
"clustered", "regular"),
method=c("asymptotic", "MonteCarlo"),
nsim=999)
"ppp"
).hopskel
is a single number. The value of hopskel.test
is an object of class "htest"
representing the outcome of the test. It can be printed.
If the point pattern X
contains n
points, we first compute the nearest-neighbour distances
$P_1, \ldots, P_n$
so that $P_i$ is the distance from the $i$th data
point to the nearest other data point. Then we
generate another completely random pattern U
with
the same number n
of points, and compute for each point of U
the distance to the nearest point of X
, giving
distances $I_1, \ldots, I_n$.
The test statistic is
$$A = \frac{\sum_i P_i^2}{\sum_i I_i^2}$$
The null distribution of $A$ is roughly
an $F$ distribution with shape parameters $(2n,2n)$.
(This is equivalent to using the test statistic $H=A/(1+A)$
and referring $H$ to the Beta distribution with parameters
$(n,n)$).
The function hopskel
calculates the Hopkins-Skellam test statistic
$A$, and returns its numeric value. This can be used as a simple
summary of spatial pattern: the value $H=1$ is consistent
with Complete Spatial Randomness, while values $H < 1$ are
consistent with spatial clustering, and values $H > 1$ are consistent
with spatial regularity.
The function hopskel.test
performs the test.
If method="asymptotic"
(the default), the test statistic $H$
is referred to the $F$ distribution. If method="MonteCarlo"
,
a Monte Carlo test is performed using nsim
simulated point
patterns.
clarkevans
,
clarkevans.test
,
nndist
,
nncross
hopskel(redwood)
hopskel(redwood)
hopskel.test(redwood, alternative="clustered")
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