P_cge_aeq: Probability of observing the ith nearest neighbour at a...
In knnIndep: Independence tests and benchmarks

Description Usage Arguments Details Value Author(s) See Also Examples

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 $P(d_i >= c, d_(i-1) = a)$

1	P_cge_aeq(i, c, a, k, N)

`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

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)

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

Sebastian Dümcke duemcke@mpipz.mpg.de

P_ceq, Pc_givena