scholarly journals Two-Dimensional Bayesian Information Criteria for Spatial Poisson Point Process (Case Study: Spatial Distribution Modeling of a Tree Species in Barro Colorado Island)

2021 ◽  
Author(s):  
Sigit Prabowo ◽  
Achmad Choiruddin ◽  
Nur Iriawan
Keyword(s):  
Spatial Distribution ◽  
Point Process ◽  
Tree Species ◽  
Poisson Point Process ◽  
Information Criteria ◽  
Barro Colorado Island ◽  
Two Dimensional ◽  
Distribution Modeling

Extremes for shot noise processes with heavy tailed amplitudes

1997 ◽  
Vol 34 (03) ◽  
pp. 643-656 ◽  
Author(s):  
William P. McCormick
Keyword(s):  
Point Process ◽  
Shot Noise ◽  
Renewal Process ◽  
Poisson Point Process ◽  
Point Processes ◽  
Extremal Index ◽  
Two Dimensional ◽  
Limiting Behavior ◽  
Local Maxima ◽  
Heavy Tailed

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k } are the points of a renewal process and {Ak } are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

scholarly journals Semi-Infinite Paths of the Two-Dimensional Radial Spanning Tree

2013 ◽  
Vol 45 (4) ◽  
pp. 895-916 ◽  
Author(s):  
François Baccelli ◽  
David Coupier ◽  
Viet Chi Tran
Keyword(s):  
Point Process ◽  
Infinite Number ◽  
Spanning Tree ◽  
Poisson Point Process ◽  
Two Dimensional ◽  
Infinite Path ◽  
Intersection Points

We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius r grows sublinearly with r. Then we prove that in each (deterministic) direction there exists, with probability 1, a unique semi-infinite path, framed by an infinite number of other semi-infinite paths of close asymptotic directions. The set of (random) directions in which there is more than one semi-infinite path is dense in [0, 2π). It corresponds to possible asymptotic directions of competition interfaces. We show that the RST can be decomposed into at most five infinite subtrees directly connected to the root. The interfaces separating these subtrees are studied and simulations are provided.

Extremes for shot noise processes with heavy tailed amplitudes

1997 ◽  
Vol 34 (3) ◽  
pp. 643-656 ◽  
Author(s):  
William P. McCormick
Keyword(s):  
Point Process ◽  
Shot Noise ◽  
Renewal Process ◽  
Poisson Point Process ◽  
Point Processes ◽  
Extremal Index ◽  
Two Dimensional ◽  
Limiting Behavior ◽  
Local Maxima ◽  
Heavy Tailed

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k} are the points of a renewal process and {Ak} are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

scholarly journals Two-dimensional spatial distribution modeling of sprinkler irrigation

Revista CERES ◽  
2021 ◽  
Vol 68 (4) ◽  
pp. 257-266
Author(s):  
João Carlos Ferreira Borges Júnior ◽  
Camilo de Lelis Teixeira de Andrade
Keyword(s):  
Spatial Distribution ◽  
Sprinkler Irrigation ◽  
Two Dimensional ◽  
Distribution Modeling

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (2) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (02) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

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