This session is concerned with summary statistics for spacings and interpoint distances. The lecturer’s R script is available here (right click and save).
For the swedishpines data:
Calculate the estimate of the nearest neighbour distance distribution function (G) using Gest.
Plot the estimate of (G(r)) against (r).
Plot the estimate of (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.
For the swedishpines data:
Calculate the estimate of the nearest neighbour distance distribution function (F) using Fest.
Plot the estimate of (F(r)) against (r).
Plot the estimate of (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.