# hopskel

##### Hopkins-Skellam Test

Perform the Hopkins-Skellam test of Complete Spatial Randomness, or simply calculate the test statistic.

- Keywords
- htest, spatial, nonparametric

##### Usage

`hopskel(X)`hopskel.test(X, ...,
alternative=c("two.sided", "less", "greater",
"clustered", "regular"),
method=c("asymptotic", "MonteCarlo"),
nsim=999)

##### Arguments

- X
- Point pattern (object of class
`"ppp"`

). - alternative
- String indicating the type of alternative for the hypothesis test. Partially matched.
- method
- Method of performing the test. Partially matched.
- nsim
- Number of Monte Carlo simulations to perform, if a Monte Carlo p-value is required.
- ...
- Ignored.

##### Details

Hopkins and Skellam (1954) proposed a test of Complete Spatial Randomness based on comparing nearest-neighbour distances with point-event distances.

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.

##### Value

- The value of
`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.

##### References

Hopkins, B. and Skellam, J.G. (1954)
A new method of determining the type of distribution
of plant individuals. *Annals of Botany* **18**,
213--227.

##### See Also

##### Examples

```
hopskel(redwood)
hopskel(redwood)
hopskel.test(redwood, alternative="clustered")
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*