On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour
Keyword(s):
In a homogeneous Poisson process in Rd, consider an arbitrary point X and let Y be its kth nearest neighbour. Denote by Rk the rank of X in the proximity order defined by Y, i.e., Rk = j if X is the jth nearest neighbour to Y. A representation for Rk in terms of a sum of independent random variables is obtained, and the limiting distribution of Rk, as k →∞, is shown to be normal. This result generalizes to mixtures of Poisson processes.
On the probability that a random point is the jth nearest neighbour to its own kth nearest neighbour
1986 ◽
Vol 23
(01)
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pp. 221-226
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1969 ◽
Vol 6
(02)
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pp. 453-458
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Keyword(s):
1983 ◽
Vol 20
(01)
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pp. 202-208
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2003 ◽
Vol 40
(03)
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pp. 807-814
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1992 ◽
Vol 112
(3)
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pp. 613-629
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2004 ◽
Vol 53
(2)
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pp. 226-237
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