# 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

1 | ```
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 <= c |

`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 |

### 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)

### Value

Probability vector

### Author(s)

Sebastian Dümcke duemcke@mpipz.mpg.de

### See Also

`P_cge_ale`

, `P_ceq`

### Examples

1 | ```
Pc_givena4nn(10,2:7,1:6,rep(0,6),rep(1,6),20)
``` |

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