scholarly journals Testing hypotheses on population dynamics: A test for the inhomogeneous Poisson point process model

2017 ◽  
Author(s):  
Niklas Hohmann
Keyword(s):  
Population Dynamics ◽  
Point Process ◽  
Poisson Point Process ◽  
Process Model ◽  
Confidence Regions ◽  
Significance Level ◽  
Spatial Dimensions ◽  
Rate Functions ◽  
Inhomogeneous Poisson Point Process

AbstractIn this paper, a test for hypotheses on population dynamics is presented alongside an implementation of said test for R. The test is based on the assumption that the sample, consisting of points on a time axis, is a realization of a Poisson point process (PPP). There are no restrictions on the shapes of the rate functions that are regulating the PPP, type 2 errors can be calculated and the test is optimal in the sense that it is a uniform most powerful (UMP) test. So for every significance level a, the presented test has a lower type 2 error than every other test having the same significance level a. The test is applicable to all models based on PPPs, including models in spatial dimensions. It can be generalized and expanded in different ways, such as testing larger hypotheses, incorporating prior knowledge, and constructing confidence regions that can be used to obtain upper or lower bounds on rate functions.

scholarly journals Approximate decomposition of some modulated-Poisson Voronoi tessellations

2003 ◽  
Vol 35 (4) ◽  
pp. 847-862 ◽  
Author(s):  
Bartłomiej Błaszczyszyn ◽  
René Schott
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Voronoi Tessellation ◽  
Distribution Functions ◽  
Voronoi Tessellations ◽  
Intensity Measures ◽  
Voronoi Cells ◽  
True Value ◽  
Homogeneous Models ◽  
Inhomogeneous Poisson Point Process

We consider the Voronoi tessellation of Euclidean space that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the space. Considering the Voronoi cells as marks associated with points of the point process, we prove that the intensity measure (mean measure) of the marked Poisson point process admits an approximate decomposition formula. The true value is approximated by a mixture of respective intensity measures for homogeneous models, while the explicit upper bound for the remainder term can be computed numerically for a large class of practical examples. By the Campbell formula, analogous approximate decompositions are deduced for the Palm distributions of individual cells. This approach makes possible the analysis of a wide class of inhomogeneous-Poisson Voronoi tessellations, by means of formulae and estimates already established for homogeneous cases. Our analysis applies also to the Poisson process modulated by an independent stationary random partition, in which case the error of the approximation of the double-stochastic-Poisson Voronoi tessellation depends on some integrated linear contact distribution functions of the boundaries of the partition elements.

scholarly journals Interference cancelation for high-density fifth-generation relaying network using stochastic geometrical approach

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771985587 ◽  
Author(s):  
MHD Nour Hindia ◽  
Faizan Qamar ◽  
Talib Abbas ◽  
Kaharudin Dimyati ◽  
Mohamad Sofian Abu Talip ◽  
...  
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Process Model ◽  
Success Probability ◽  
Relay Node ◽  
Ergodic Capacity ◽  
Base Station ◽  
High Density ◽  
Geometrical Approach ◽  
Fifth Generation

In order to resolve the issue of coverage limitation for the future fifth-generation network, deploying a relay node within a cell is one of the most capable and cost-effective solution, which not only enhances the coverage but also improves the spectral efficiency. However, this solution leads to the undesired interferences from nearby base station and relay nodes that affects user’s signal-to-interference-plus-noise ratio and can cause the ambiguous received signal at the user end. In this article, we have analyzed a relay-based interference-limited network at millimeter wave frequency and proposed a Poisson point process–based model using a stochastic geometrical approach. The results for the proposed Poisson point process model have been evaluated in terms of success probability, network ergodic capacity, and outage probability, compared with the ideal grid model and conventional multiple-antenna ultra-dense network model. The results proved that the success probability and ergodic capacity for the proposed model are 3.5% and 2.3% higher as compared to the most commonly used model for the high-density network, respectively. Furthermore, the results have been analyzed at different multiple-input-multiple-output antenna configuration, which validates the model in the improvement of overall network performance even for higher number of antennas.

scholarly journals Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation

2009 ◽  
Vol 12 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Paulo Rangel Rios ◽  
Douglas Jardim ◽  
Weslley Luiz da Silva Assis ◽  
Tatiana Caneda Salazar ◽  
Elena Villa
Keyword(s):  
Cellular Automata ◽  
Analytical Solution ◽  
Point Process ◽  
Poisson Point Process ◽  
Inhomogeneous Poisson Point Process

scholarly journals Approximate decomposition of some modulated-Poisson Voronoi tessellations

2003 ◽  
Vol 35 (04) ◽  
pp. 847-862
Author(s):  
Bartłomiej Błaszczyszyn ◽  
René Schott
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Voronoi Tessellation ◽  
Distribution Functions ◽  
Voronoi Tessellations ◽  
Intensity Measures ◽  
Voronoi Cells ◽  
True Value ◽  
Homogeneous Models ◽  
Inhomogeneous Poisson Point Process

We consider the Voronoi tessellation of Euclidean space that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the space. Considering the Voronoi cells as marks associated with points of the point process, we prove that the intensity measure (mean measure) of the marked Poisson point process admits an approximate decomposition formula. The true value is approximated by a mixture of respective intensity measures for homogeneous models, while the explicit upper bound for the remainder term can be computed numerically for a large class of practical examples. By the Campbell formula, analogous approximate decompositions are deduced for the Palm distributions of individual cells. This approach makes possible the analysis of a wide class of inhomogeneous-Poisson Voronoi tessellations, by means of formulae and estimates already established for homogeneous cases. Our analysis applies also to the Poisson process modulated by an independent stationary random partition, in which case the error of the approximation of the double-stochastic-Poisson Voronoi tessellation depends on some integrated linear contact distribution functions of the boundaries of the partition elements.

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