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Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques [PDF]
EntropyWe study nearest-neighbor-based estimators of Tsallis entropy associated with Poisson and binomial point processes on general metric measure spaces. In this study, by combining existing stabilization methods with the validation of the estimator’s local k-
Mehmet Sıddık Çadırcı +1 more
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The two-parameter Poisson–Dirichlet point process
Bernoulli, 2009 The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the associated point process (that is, the random point process obtained by regarding the masses as points in the ...
Kenji Handa
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Navigation on a Poisson point process
Annals of Applied Probability, 2008 On a locally finite point set, a navigation defines a path through the point set from one point to another. The set of paths leading to a given point defines a tree known as the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on $\mathbb{R}^d$.
Charles Bordenave
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Poisson Cox Point Processes for Vehicular Networks
IEEE Transactions on Vehicular Technology, 2018 This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads.
Chang-Sik Choi, François Baccelli
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The favorite point of a Poisson process
Stochastic Processes and Their Applications, 1995 Let \(N\) be a Poisson process with the unit rate, \(\xi_ t (x)\) be the occupation of \(x\) by time \(t\), i.e. \(\xi_ t (x) = \int^ t_ 0 I_{\{x\}} (N_ u) du\). The favorite point of \(N\) up to time \(t\) is defined as follows: \[ X_ t = \min \bigl \{k \geq 0 : \xi_ t (k) \geq \xi_ t (i) \text{ for all } i \geq 0 \bigr\}.
, Thomas M Lewis
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The radial spanning tree of a Poisson point process
Annals of Applied Probability, 2007 We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments to analyze local functionals of the random tree such as the distribution of the length of the edges or the mean ...
Charles Bordenave
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Spatial Pattern Simulation of Antenna Base Station Positions Using Point Process Techniques
Telecom, 2022 Spatial statistics is a powerful tool for analyzing data that are illustrated as points or positions in a regular or non-regular state space. Techniques that are proposed to investigate the spatial association between neighboring positions are based on ...
Stelios Zimeras
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Modeling Scheme of Multi-Layer Heterogeneous Network for Dense Hotspot Area [PDF]
Jisuanji gongcheng, 2021 To address the heterogeneity in Base Station(BS) deployment and the coupling between User Equipment (UE) and BS in the hotspot communication scenario of the fifth-generation(5G)/beyond 5G(B5G) networks,this paper proposes a three-layer heterogeneous ...
Lü Yaping, JIA Xiangdong, CHEN Yuwan, LU Yi
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Poissonization Principle for a Class of Additive Statistics
Mathematics, 2022 In this paper, we consider a class of additive functionals of a finite or countable collection of the group frequencies of an empirical point process that corresponds to, at most, a countable partition of the sample space.
Igor Borisov, Maman Jetpisbaev
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Properties of a Random Bipartite Geometric Associator Graph Inspired by Vehicular Networks
Entropy, 2023 We consider a point process (PP) generated by superimposing an independent Poisson point process (PPP) on each line of a 2D Poisson line process (PLP). Termed PLP-PPP, this PP is suitable for modeling networks formed on an irregular collection of lines ...
Kaushlendra Pandey +3 more
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