Probabilities for a $k$th Nearest Neighbor Problem on the Line
Wallenstein, Sylvan R. ; Naus, Joseph I.
Ann. Probab., Tome 1 (1973) no. 5, p. 188-190 / 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 $n > N/2$, and for $n \leqq N/2, p = 1/L, L$ an integer. This paper finds the distribution of $p_n$, for all $n, N,$ and $p$.
Publié le : 1973-02-14
Classification:  60,  E05,  Coincidences,  clusters,  nearest neighbor distances,  maximum clusters,  smallest intervals 
@article{1176997037,
     author = {Wallenstein, Sylvan R. and Naus, Joseph I.},
     title = {Probabilities for a $k$th Nearest Neighbor Problem on the Line},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 188-190},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176997037}
}

Wallenstein, Sylvan R.; Naus, Joseph I. Probabilities for a $k$th Nearest Neighbor Problem on the Line. Ann. Probab., Tome 1 (1973) no. 5, pp.  188-190. http://gdmltest.u-ga.fr/item/1176997037/