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MaternPointProcess[μ,λ,rm,d]
represents a Matérn cluster point process with density μ, cluster mean λ and radius rm in .
Details Examplesopen allclose all Basic Examples (3)Sample from a Matérn point process over a unit disk:
Sample from a Matérn point process over a unit ball:
Sample from a Matérn point process over a geo region:
Scope (3)Sample from a valid region whose dimension is equal to its embedding dimension:
Sample from a Matérn point process in the region and visualize the points:
Simulate a point configuration from a Matérn point process:
Use the "FindClusters" method to estimate a point process model:
Compare the Ripley measure between the original process and the estimated model:
Pair correlation function of a Matérn point process:
Visualize the function with given parameter values:
Properties & Relations (5)PointCountDistribution is known:
The probability density histogram:
Ripley's and Besag's for Matérn point process in 2D:
Ripley's of Matérn point process is larger than for a Poisson point process:
Compare to the Poisson point process:
Besag's of Matérn point process is larger than for a Poisson point process:
Compare to the Poisson point process:
Pair correlation of Matérn point process is larger than 1:
Compare to homogeneous Poisson point process:
Possible Issues (1)The estimation algorithm splitting the point data into clusters may find a different cluster radius than in a model used to create a given point collection:
Therefore, specifying a smaller cluster radius than is inferred from the data will result in the failure of finding a point process model:
Wolfram Research (2020), MaternPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/MaternPointProcess.html. TextWolfram Research (2020), MaternPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/MaternPointProcess.html.
CMSWolfram Language. 2020. "MaternPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaternPointProcess.html.
APAWolfram Language. (2020). MaternPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaternPointProcess.html
BibTeX@misc{reference.wolfram_2025_maternpointprocess, author="Wolfram Research", title="{MaternPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MaternPointProcess.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_maternpointprocess, organization={Wolfram Research}, title={MaternPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/MaternPointProcess.html}, note=[Accessed: 12-July-2025 ]}
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