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.