# Lab 8: Spacing and distances

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:

1. Calculate the estimate of the nearest neighbour distance distribution function G using `Gest`.

2. Plot the estimate of G(r) against r.

3. Plot the estimate of G(r) against the theoretical (Poisson) value Gpois(r)=1 − exp(−λπr2).

4. 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:

1. Calculate the estimate of the nearest neighbour distance distribution function F using `Fest`.

2. Plot the estimate of F(r) against r.

3. Plot the estimate of F(r) against the theoretical (Poisson) value Fpois(r)=1 − exp(−λπr2).

4. 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.