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

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Description

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

Usage

1
P_cge_aeq(i, c, a, k, 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 ith NN was observed. a <= c

k

vector, number of previous NNs at distance a

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, entries with value -1 if the probability does not exist

Author(s)

Sebastian Dümcke duemcke@mpipz.mpg.de

See Also

P_ceq, Pc_givena

Examples

1
P_cge_aeq(10,4:8,2:6,rep(1,5),30)