BinomialPointProcess

BinomialPointProcess[n,reg]

represents a binomial point process with n points in the region reg.

Details

Examples

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Basic Examples  (2)

Sample a BinomialPointProcess:

Sample several realizations:

Scope  (2)

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

Create a binomial point process on a geo region:

Simulate points on the same region:

Applications  (1)

A shooter at a range shoots 12 bullets at random at a round target of diameter 1 meter. Simulate possible bullet patterns:

Properties & Relations  (4)

The number of points in a BinomialPointProcess is defined by n:

Simulate BinomialPointProcess over a unit disk:

The corresponding PointCountDistribution over a bounded subset:

Compare the histogram of point counts in the subset with the PDF:

Fit a BinomialDistribution to the point counts:

Test goodness of fit:

Test against theoretical distribution:

PointCountDistribution over region covering:

Define a three-set covering:

Point count distribution for the covering:

Compute void probabilities for a binomial point process:

For a rectangle:

Binomial point process is stationary—the intensity is translation invariant:

Point count distribution in a subregion:

Point count distribution in the translated subregion:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_binomialpointprocess, author="Wolfram Research", title="{BinomialPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/BinomialPointProcess.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_binomialpointprocess, organization={Wolfram Research}, title={BinomialPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/BinomialPointProcess.html}, note=[Accessed: 21-February-2025 ]}