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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
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