Probability of observing the ith nearest neighbour at the same distance or larger as the (i-1)th nearest neighbour

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Description

This function gives the probability of observing the ith nearest neighbour distance larger or equal to c, and the (i-1)th nearest neighbour at distance c, $P(d_i >= c, d_(i-1) = c)$.

Usage

1
P_ceq(i, c, N)

Arguments

i

numeric, which nearest neighbour to consider

c

vector, the distance at which the ith NN was observed

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, Pc_givena

Examples

1
P_ceq(10,1:10,25)