ThomasPointProcess

ThomasPointProcess[μ,λ,σ,d]

represents a Thomas cluster point process with density μ, cluster mean λ and scale parameter σ in R^(d).

Details

Examples

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Basic Examples  (4)

Sample from a Thomas point process over a unit disk:

Sample from a Thomas point process over a unit ball:

Sample from a Thomas point process over a geo region:

Pair correlation function of a Thomas point process:

Visualize the function with given parameter values:

Scope  (2)

Sample from any valid RegionQ, whose RegionEmbeddingDimension is equal to its RegionDimension:

Check the region conditions:

Sample points:

Simulate a point configuration from a Thomas point process:

Use the "FindClusters" method to estimated a point process model:

Compare Ripley's measure between the original process and the estimated model:

Properties & Relations  (5)

PointCountDistribution is known:

Mean and variance:

Plot the PDF:

Simulate the distribution:

The probability density histogram:

Ripley's and Besag's for a Thomas point process in 2D:

Visualize:

Ripley's of the Thomas point process is larger than for a Poisson point process:

In 2D and fixed density:

Besag's of the Thomas point process is greater than of the Poisson point process:

In 2D and fixed density:

The pair correlation function of a Thomas point process is greater than 1:

Compare to the homogeneous Poisson point process:

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

Text

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

BibTeX

@misc{reference.wolfram_2020_thomaspointprocess, author="Wolfram Research", title="{ThomasPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ThomasPointProcess.html}", note=[Accessed: 17-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_thomaspointprocess, organization={Wolfram Research}, title={ThomasPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/ThomasPointProcess.html}, note=[Accessed: 17-January-2021 ]}

CMS

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

APA

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