P_cge_aeq:
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
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
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<="" code="">
k
vector, number of previous NNs at distance a
N
numeric, size of the dataset
Value
Probability vector, entries with value -1 if the probability does not exist
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)