represents an inhomogeneous Poisson point process with density function in .
- InhomogeneousPoissonPointProcess is also known as a nonstationary Poisson point process or an independent scattering point process.
- Typical uses include modeling varying density that depends only on the location , such as varying growth conditions.
- InhomogeneousPoissonPointProcess generates points in a region according to the specified density function μ with no point interactions.
- With density function μ, the point count in an observation region is distributed as PoissonDistribution with mean .
- Density function μ can be given as:
func a function of vectors geofunc a function of geo locations PointDensityFunction density function from point collections
- The number of points in disjoint regions for a Poisson point process are independent , where are non-negative integers.
- A point configuration with density function μ in an observation region with volume has density function with respect to PoissonPointProcess[1,d].
- The Papangelou conditional density for adding a point to a point configuration is for an inhomogeneous Poisson point process with density function μ.
- The density function can be any positive integrable function in and d can be any positive integer.
- InhomogeneousPoissonPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.
Examplesopen allclose all
Basic Examples (4)
Sample from an InhomogeneousPoissonPointProcess:
Sample from an InhomogeneousPoissonPointProcess defined on the surface of the Earth:
PointCountDistribution is invariant with respect to a rotation about the origin:
Sample from an InhomogeneousPoissonPointProcess using different methods:
Properties & Relations (5)
Inhomogeneous Poisson point process with constant density autoevaluates to PoissonPointProcess:
The densities as expressed via PointCountDistribution differ:
Wolfram Research (2020), InhomogeneousPoissonPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/InhomogeneousPoissonPointProcess.html.
Wolfram Language. 2020. "InhomogeneousPoissonPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InhomogeneousPoissonPointProcess.html.
Wolfram Language. (2020). InhomogeneousPoissonPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InhomogeneousPoissonPointProcess.html