RipleyRassonRegion

RipleyRassonRegion[pdata]

gives an estimated observation based on the point data pdata.

Details

  • RipleyRassonRegion is typically used to automatically derive an observation region from a point collection when no such region is provided. It is strongly suggested to obtain the correct observation region in the original data collection if at all possible, in order to get correct spatial statistics.
  • RipleyRassonRegion is a centrally rescaled version of the convex hull of the set of points, effectively given by ScalingTransform[{s,s,…},c], where c is the region centroid of the convex hull.
  • For geographic regions, the corresponding operation is done on the projection.
  • The resulting region is an unbiased estimator of the true region under the assumption that the point collection was generated by a PoissonPointProcess. It may not be a very representative observation region for clustered and other forms of point collections.
  • The point data pdata can have the following forms:
  • {p1,p2,…}points pi
    GeoPosition[…],GeoPositionXYZ[…],…geographic points

Examples

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Basic Examples  (2)

Compute RipleyRassonRegion from random points in a unit disk:

Compute RipleyRassonRegion from random locations on the surface of the Earth:

Possible Issues  (1)

Computation of RipleyRassonRegion for a point configuration of InhomogeneousPoissonPointProcess will depend strongly on a given realization:

Compare Ripley–Rasson region estimates:

Wolfram Research (2020), RipleyRassonRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/RipleyRassonRegion.html.

Text

Wolfram Research (2020), RipleyRassonRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/RipleyRassonRegion.html.

CMS

Wolfram Language. 2020. "RipleyRassonRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RipleyRassonRegion.html.

APA

Wolfram Language. (2020). RipleyRassonRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RipleyRassonRegion.html

BibTeX

@misc{reference.wolfram_2023_ripleyrassonregion, author="Wolfram Research", title="{RipleyRassonRegion}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}", note=[Accessed: 16-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_ripleyrassonregion, organization={Wolfram Research}, title={RipleyRassonRegion}, year={2020}, url={https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}, note=[Accessed: 16-April-2024 ]}