# rknn

0th

Percentile

##### Theoretical Distribution of Nearest Neighbour Distance

Density, distribution function, quantile function and random generation for the random distance to the $$k$$th nearest neighbour in a Poisson point process in $$d$$ dimensions.

Keywords
distribution, spatial
##### 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.

##### References

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

• dknn
• pknn
• qknn
• rknn
##### Examples
# NOT RUN {
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)
# }

Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)

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