NeymanScottPointProcess

NeymanScottPointProcess[μ,λ,rdist,d]

represents a Neyman–Scott point process with density function μ, cluster mean λ and radial cluster point distribution rdist in .

NeymanScottPointProcess[μ,λ,mdist,d]

uses a multivariate cluster point distribution mdist in .

Details

Examples

open allclose all

Basic Examples  (4)

Sample from a Neyman–Scott point process with a radial cluster distribution:

Sample from a 3D Neyman–Scott point process over a unit ball with multivariate cluster distribution:

Sample over a geographical region:

Valid density functions are the same as for InhomogeneousPoissonPointProcess:

Scope  (2)

Sample over a valid region whose dimension is equal to its embedding dimension:

Sample from a Neyman–Scott point process in the region and visualize the points:

Simulate a point configuration from a Neyman–Scott point process:

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

Properties & Relations  (1)

PointCountDistribution is known:

Mean and variance:

Plot the PDF:

Simulate the distribution:

The probability density histogram:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_neymanscottpointprocess, author="Wolfram Research", title="{NeymanScottPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/NeymanScottPointProcess.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_neymanscottpointprocess, organization={Wolfram Research}, title={NeymanScottPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/NeymanScottPointProcess.html}, note=[Accessed: 21-February-2025 ]}