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

1	P_ceq(i, c, N)

`i`	numeric, which nearest neighbour to consider
`c`	vector, the distance at which the ith NN was observed
`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

Sebastian Dümcke duemcke@mpipz.mpg.de

P_cge_ale, Pc_givena