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 \(\hat G(r)\) 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.