Central probabilty

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Description

Probability of observing r NN distances at distance c, all previous NN distances at distance < c and all following NN distances at a distance > c

Usage

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parameters(r, i0, c, N)
kr(r, i0, c)

Arguments

r

the number of points that are at the same distance c

i0

which i0-th nearest neighbour we are considering.

c

the distance of the i-th nearest neighbour

N

sample size

Value

for kr the number of possibilities to place r points onto the same distance when we already observed i0 points at a smaller distance

for parameters the probability of observing r NN distances at distance c, all previous NN distances at distance < c and all following NN distances at a distance > c

Author(s)

Sebastian D├╝mcke duemcke@mpipz.mpg.de

Examples

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knnIndep:::kr(3,5,6)
knnIndep:::parameters(3,5,6,20)