Orlov, Oleg P. Limit distributions of the maximal distance to the nearest neighbour. (English. Russian original) Zbl 1448.60059 Discrete Math. Appl. 29, No. 6, 373-381 (2019); translation from Diskretn. Mat. 30, No. 3, 88-98 (2018). Summary: For sets of iid random points having a uniform (in a definite sense) distribution on the arbitrary metric space a maximal distance to the nearest neighbour is considered. By means of the Chen-Stein method new limit theorems for this random variable is proved. For random uniform samples from the set of binary cube vertices analogous results are obtained by the methods of moments. MSC: 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics Keywords:random points in metric space; maximal distance to nearest neighbour; limit distributions; binary cube PDF BibTeX XML Cite \textit{O. P. Orlov}, Discrete Math. Appl. 29, No. 6, 373--381 (2019; Zbl 1448.60059); translation from Diskretn. Mat. 30, No. 3, 88--98 (2018) Full Text: DOI References: [1] Barbour A. D., Chen Louis H. Y., An introduction to Stein’s method, Singapore Univ. Press and World Scientific Publ. Co. Pte. Ltd, 2005. · Zbl 1072.62007 [2] Barbour A. D., Holst L., Janson S., Poisson approximation, Clarendon press, Oxford, 1992. [3] Zubkov A. M., Orlov O. P., “Limit distributions of extremal distances to the nearest neighbor”, Discrete Math. Appl., 28:3 (2018), 189-199. · Zbl 1395.60031 [4] Hoeffding W., “Probability inequalities for sums of bounded random variables”, J. Amer. Stat. Assoc., 58:301 (1963), 13-30. · Zbl 0127.10602 [5] Henze N., “The limit distribution for maxima of ”weighted“ rth-nearest-neighbour distances”, J. Appl. Probab., 19:2 (1982), 344-354. · Zbl 0484.62034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.