rknn {spatstat} | R Documentation |
Density, distribution function, quantile function and random generation for the random distance to the kth nearest neighbour in a Poisson point process in d dimensions.
dknn(x, k = 1, d = 2, lambda = 1) pknn(q, k = 1, d = 2, lambda = 1) qknn(p, k = 1, d = 2, lambda = 1) rknn(n, k = 1, d = 2, lambda = 1)
x,q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to be generated. |
k |
order of neighbour. |
d |
dimension of space. |
lambda |
intensity of Poisson point process. |
In a Poisson point process in d-dimensional space, let the random variable R be the distance from a fixed point to the k-th nearest random point, or the distance from a random point to the k-th nearest other random point.
Then R^d has a Gamma distribution with shape parameter k and rate lambda * alpha where alpha is a constant (equal to the volume of the unit ball in d-dimensional space). See e.g. Cressie (1991, page 61).
These functions support calculation and simulation for the distribution of R.
A numeric vector:
dknn
returns the probability density,
pknn
returns cumulative probabilities (distribution function),
qknn
returns quantiles,
and rknn
generates random deviates.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Cressie, N.A.C. (1991) Statistics for spatial data. John Wiley and Sons, 1991.
x <- seq(0, 5, length=20) densities <- dknn(x, k=3, d=2) cdfvalues <- pknn(x, k=3, d=2) randomvalues <- rknn(100, k=3, d=2) deciles <- qknn((1:9)/10, k=3, d=2)