# VarianceGammaPointProcess

VarianceGammaPointProcess[μ,λ,α,β,d]

represents a variance gamma cluster point process with density μ, cluster mean λ and shape parameters α and β in .

# Examples

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## Basic Examples(4)

Sample from a variance gamma point process over a unit disk:

Sample from a variance gamma point process over a unit ball:

Sample from a variance gamma point process over a geo region:

Pair correlation function of a variance gamma 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 variance gamma 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)

The PointCountDistribution is known:

Mean and variance:

Plot the PDF:

Simulate the distribution:

The probability density histogram:

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

Ripley's of a variance gamma point process is larger than for a Poisson point process:

Compare to a Poisson point process:

Besag's of a variance gamma point process is larger than for a Poisson point process:

Compare to a Poisson point process:

The pair correlation of a variance gamma point process is larger than 1:

Compare to a homogeneous Poisson point process:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_variancegammapointprocess, author="Wolfram Research", title="{VarianceGammaPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/VarianceGammaPointProcess.html}", note=[Accessed: 16-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_variancegammapointprocess, organization={Wolfram Research}, title={VarianceGammaPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/VarianceGammaPointProcess.html}, note=[Accessed: 16-April-2024 ]}