Test of a point pattern against Complete Spatial Randomness

Tests the point pattern against CSR using values of the K function

Usage

Ktest(X, r)

Arguments

X: A point pattern (ppp.object). Marks are ignored. The window must be a rectangle sensu spatstat (tested by is.rectangle).
r: A vector of distances.

Details

The test returns the risk to reject CSR erroneously, i.e. the p-value of the test, based on the distribution of the K function.

If r includes 0, it will be silently removed because no neighbor point can be found at distance 0. The longer r, the more accurate the test is in theory but at the cost of computation time first, and of computation accuracy then because a matrix of size the length of r must be inverted. 10 values in r seems to be a reasonable choice.

Value

A p-value.

References

Lang, G. and Marcon, E. (2013). Testing randomness of spatial point patterns with the Ripley statistic. ESAIM: Probability and Statistics. 17: 767-788.

Marcon, E., S. Traissac, and Lang, G. (2013). A Statistical Test for Ripley's Function Rejection of Poisson Null Hypothesis. ISRN Ecology 2013(Article ID 753475): 9.

Author

Gabriel Lang <Gabriel.Lang@agroparistech.fr>, Eric Marcon<Eric.Marcon@agroparistech.fr>

Examples

# Simulate a Matern (Neyman Scott) point pattern
nclust <- function(x0, y0, radius, n) {
  return(runifdisc(n, radius, centre=c(x0, y0)))
}
X <- rNeymanScott(20, 0.1, nclust, radius=0.2, n=5)
autoplot(as.wmppp(X))


# Test it
Ktest(X, r=seq(0.1, .5, .1))
#> [1] 0.02448668