Pc_givena4nn:
Probability of observing the ith nearest neighbour at distance greater or equal
c given the 4 previous nearest neighbours
Description
This function gives the probability of observing the ith nearest neighbour at
distance c given the previous 4 nearest neighbour distances, $P(d_i >= x | d_(i-1), d_(i-2), d_(i-3), d_(i-4))$
Usage
Pc_givena4nn(i, c, a, k1, k2, 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 (i-1)th NN was observed, a
k1
vector, number of previous neighbhour at distance d_i
k2
vector, number of preivous neighbhours at distance d_(i-1)
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" (PLoS ONE 2014)