represents a Neyman–Scott point process with density function μ, cluster mean λ and radial cluster point distribution rdist in .
uses a multivariate cluster point distribution mdist in .
- NeymanScottPointProcess is also known as the center-satellite process.
- NeymanScottPointProcess models clustered point configurations with centers placed according to an inhomogeneous Poisson point process and cluster points distributed around the centers according to a cluster distribution.
- Typical uses include herds of animals in the wild, clusters of seedlings around a parent tree, modeling bombing patterns and insect larvae patterns.
- Cluster centers are placed according to InhomogeneousPoissonPointProcess with density function in .
- The point count of a cluster is distributed according to PoissonDistribution with mean λ.
- Cluster points following an isotropic distribution are most easily specified using a radial distribution rdist.
- A general cluster distribution can be specified using a multivariate distribution mdist.
- NeymanScottPointProcess is a general Poisson cluster process; common Poisson cluster processes have dedicated functions and are easier and more efficient to use when applicable.
process radial distribution characteristic MaternPointProcess uniform cluster points ThomasPointProcess normal cluster points CauchyPointProcess heavy tail cluster points VarianceGammaPointProcess normal and gamma mixture cluster points
- NeymanScottPointProcess allows λ to be any positive real number and and d to be any positive integer.
- The following settings can be used for PointProcessEstimator for estimating NeymanScottPointProcess:
"FindClusters" use FindClusters function "MethodOfMoments" use a homogeinity measure to estimate the parameters
- NeymanScottPointProcess can be used with such functions as RipleyK, PointCountDistribution and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (3)
Properties & Relations (1)
PointCountDistribution is known:
Wolfram Research (2020), NeymanScottPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/NeymanScottPointProcess.html.
Wolfram Language. 2020. "NeymanScottPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NeymanScottPointProcess.html.
Wolfram Language. (2020). NeymanScottPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NeymanScottPointProcess.html