Probability of observing the ith nearest neighbour at distance greater or equal c given the (i-1)th nearest neighbour at distance a

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Description

This function gives the probability of observing the ith nearest neighbour at distance c given the (i-1)th nearest neighbour at distance a, $P(d_i >= x | d_(i-1) = a)$

Usage

1
Pc_givena(i, c, a, N)

Arguments

i

numeric, which nearest neighbour to consider

c

vector, the distance at which the ith NN was observed

a

vector, the distance at which the (i-1)th NN was observed, a <= c

N

numeric, size of the dataset

Details

The probability is calculated by ranking the data and assuming that the data lie on a torus. For details see Dümcke et al. "A novel test for independence derived from an exact distribution of ith nearest neighbours" (manuscript in preparation)

Value

Probability vector

Author(s)

Sebastian Dümcke duemcke@mpipz.mpg.de

See Also

P_cge_ale, P_ceq

Examples

1
Pc_givena(10,2:7,1:6,20)