rknn {spatstat.random}

Theoretical Distribution of Nearest Neighbour Distance

Description

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.

Usage

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)

Arguments

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.

Details

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.

Value

A numeric vector: dknn returns the probability density, pknn returns cumulative probabilities (distribution function), qknn returns quantiles, and rknn generates random deviates.

Author(s)

Adrian Baddeley [e-mail]

and Rolf Turner [e-mail]

References

Cressie, N.A.C. (1991) Statistics for spatial data. John Wiley and Sons, 1991.

Examples

  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)