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
- 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.
Examples
open allclose allBasic 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)
Properties & Relations (1)
PointCountDistribution is known:
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