A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities
Huntington, Raymond J. ; Naus, Joseph I.
Ann. Probab., Tome 3 (1975) no. 6, p. 894-896 / Harvested from Project Euclid
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Given $N$ points distributed at random on $\lbrack 0, 1)$, let $p_n$ be the size of the smallest interval that contains $n$ points. Previous work finds $\operatorname{Pr}(p_n \leqq p)$ for all $n, N$, and rational $p$. The present note derives a new and considerably simplified formula for $\operatorname{Pr}(p_n \leqq p)$ for all $n, N$, and $p$.
Publié le : 1975-10-14
Classification:  Coincidences,  clusters,  nearest neighbor distances,  maximum clusters,  smallest intervals,  interarrival times,  60E05 
@article{1176996278,
     author = {Huntington, Raymond J. and Naus, Joseph I.},
     title = {A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 894-896},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996278}
}

Huntington, Raymond J.; Naus, Joseph I. A Simpler Expression for $K$th Nearest Neighbor Coincidence Probabilities. Ann. Probab., Tome 3 (1975) no. 6, pp.  894-896. http://gdmltest.u-ga.fr/item/1176996278/