Statistical properties of Poisson-Voronoi tessellation cells in bounded regions
| Autor: | Robert G. Aykroyd, Stuart Barber, Fatih Gezer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Discrete mathematics 021103 operations research Applied Mathematics Generalized gamma distribution 0211 other engineering and technologies 02 engineering and technology Computer Science::Computational Geometry Poisson distribution 01 natural sciences 010104 statistics & probability symbols.namesake Modeling and Simulation Bounded function Poisson point process symbols Mathematics::Metric Geometry 0101 mathematics Statistics Probability and Uncertainty Voronoi diagram Neighbourhood (mathematics) Spatial analysis Mathematics |
| ISSN: | 0094-9655 |
| Popis: | Many spatial statistics methods require neighbourhood structures such as the one determined by a Voronoi tessellation, so understanding statistical properties of Voronoi cells is crucial. While distributions of cell properties when data locations follow an unbounded homogeneous Poisson process have been studied, little attention has been given to how these properties change when a boundary is imposed. This is important when geographical data are gathered within a restricted study area, such as a national boundary or a coastline. We study the effects of imposing a boundary on the cell properties of a Poisson Voronoi tessellation. The area, perimeter and number of edges of individual cells with and without boundary conditions are investigated by simulation. Distributions of these properties differ substantially when boundaries are imposed, and these differences are affected by proximity to the boundary. We also investigate how changes in such properties when boundaries are imposed vary over two-dimensional space. |
| Databáze: | OpenAIRE |
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