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