Lab 8: Spacing and distances

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This session is concerned with summary statistics for spacings and interpoint distances.
The lecturer’s R script is available here (right click and save).

Exercise 1

For the swedishpines data:

Calculate the estimate of the nearest neighbour distance distribution function $G$ using Gest.
Plot $\hat G(r)$ against $r$
Plot $\hat G(r)$ against the theoretical (Poisson) value $G_{\mbox{pois}}(r) = 1 - \exp(-\lambda \pi r^2)$ .
Define Fisher’s variance-stabilising transformation for c.d.f.’s by
```
Phi <- function(x) asin(sqrt(x))
```
Plot the $G$ function using the formula Phi(.) ~ Phi(theo) and interpret it.

Exercise 2

For the swedishpines data:

Calculate the estimate of the nearest neighbour distance distribution function $F$ using Fest.
Plot $\hat F(r)$ against $r$
Plot $\hat F(r)$ against the theoretical (Poisson) value $F_{\mbox{pois}}(r) = 1 - \exp(-\lambda \pi r^2)$ .
Define Fisher’s variance-stabilising transformation for c.d.f.’s by
```
Phi <- function(x) asin(sqrt(x))
```
Plot the $F$ function using the formula Phi(.) ~ Phi(theo) and interpret it.