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Stats, Volume 3, Issue 1
March 2020 - 7 articles
Cover Story: This article proposes evaluating the distribution of distances between points randomly distributed in a compact set, such as point events generated by a homogeneous Poisson process. The distribution of distances between elements is important in situations where the interaction between elements depends on distance. It involves many disciplines, such as statistical physics, biology, ecology, geography, and networking. After a review of solutions proposed in the literature, this article presents a modern, general, and unified resolution method. The method is then applied to typical compact sets: segments, rectangles, disks, spheres, and hyperspheres. The article also highlights various applications of these results, for example, that variance of distances in hyperspheres tends to zero when the space dimension increases.View this paper.
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Stats - ISSN 2571-905X