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 G_pois(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 F_pois(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.