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RipleyRassonRegion
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RipleyRassonRegion

[Experimental]

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Compute RipleyRassonRegion from random points in a unit disk:

In[1]:=1
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-mdrwj0
In[2]:=2
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-yqppeq
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-baq590
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-fzzvn2
In[2]:=2
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-lap7vi
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-mu2t4w
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

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

In[36]:=36
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-wrl8v9
In[37]:=37
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-q2l3l9
In[38]:=38
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-w1fje8
In[39]:=39
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-2ll423
In[46]:=46
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-r95wry
Out[46]=46

Compare Ripley–Rasson region estimates:

In[41]:=41
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-btaznp
In[43]:=43
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https://wolfram.com/xid/0fokaytqukazwiz0tq6-i46x2r
Out[43]=43
Wolfram Research (2020), RipleyRassonRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/RipleyRassonRegion.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_ripleyrassonregion, author="Wolfram Research", title="{RipleyRassonRegion}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}", note=[Accessed: 22-June-2025 ]}

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@misc{reference.wolfram_2025_ripleyrassonregion, author="Wolfram Research", title="{RipleyRassonRegion}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}", note=[Accessed: 22-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_ripleyrassonregion, organization={Wolfram Research}, title={RipleyRassonRegion}, year={2020}, url={https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}, note=[Accessed: 22-June-2025 ]}

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@online{reference.wolfram_2025_ripleyrassonregion, organization={Wolfram Research}, title={RipleyRassonRegion}, year={2020}, url={https://reference.wolfram.com/language/ref/RipleyRassonRegion.html}, note=[Accessed: 22-June-2025 ]}