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 $$\hat G(r)$$ against $$r$$

3. Plot $$\hat G(r)$$ against the theoretical (Poisson) value $$G_{\mbox{pois}}(r) = 1 - \exp(-\lambda \pi r^2)$$.

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 $$\hat F(r)$$ against $$r$$

3. Plot $$\hat F(r)$$ against the theoretical (Poisson) value $$F_{\mbox{pois}}(r) = 1 - \exp(-\lambda \pi r^2)$$.

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.