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 |

`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`

1 | ```
P_ceq(10,1:10,25)
``` |

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