R: Theoretical Distribution of Nearest Neighbour Distance

rknn {spatstat} | R Documentation

## 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 Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### 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)

[Package spatstat version 1.63-3 Index]