PenttinenPointProcess[μ,γ,rp,d]
represents a Penttinen point process with constant intensity μ, interaction parameter γ and interaction radius rp in .


PenttinenPointProcess
PenttinenPointProcess[μ,γ,rp,d]
represents a Penttinen point process with constant intensity μ, interaction parameter γ and interaction radius rp in .
Details



- PenttinenPointProcess is also known as pairwise area interaction process.
- PenttinenPointProcess models point configurations where points have a pairwise repulsion that is log-linear in the measure of the overlap between balls around the points of radius rp, which are otherwise uniformly distributed.
- The Penttinen model is typically used when the process interaction depends on the amount of shared resources within radius rp, such as plants, trees and nests of animals.
- The Penttinen point process can be defined as a GibbsPointProcess in terms of its intensity μ and the pair potential ϕ or pair interaction h, which are both parametrized by γ and rp as follows:
-
pair potential pair interaction - Here
is the measure of overlapping balls:
-
overlapping area in overlapping volume in overlapping measure in - A point configuration
from a Penttinen point process in an observation region reg has density function
proportional to
, with respect to PoissonPointProcess[1,d].
- The Papangelou conditional density
for adding a point
to a point configuration
is
.
- PenttinenPointProcess allows μ, γ and rp to be positive numbers such that
, and d to be any positive integer.
- PenttinenPointProcess simplifies to PoissonPointProcess when
. Smaller values of
inhibit points within
.
- Possible Method settings in RandomPointConfiguration for StraussPointProcess are:
-
"MCMC" Markov chain Monte Carlo birth and death "Exact" coupling from the past - Possible PointProcessEstimator settings in EstimatedPointProcess for PenttinenPointProcess are:
-
Automatic automatically choose the parameter estimator "MaximumPseudoLikelihood" maximize the pseudo-likelihood - PenttinenPointProcess can be used with such functions as RipleyK and RandomPointConfiguration.

Examples
open all close allBasic Examples (2)
Scope (2)
Options (3)
Related Guides
History
Text
Wolfram Research (2020), PenttinenPointProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
CMS
Wolfram Language. 2020. "PenttinenPointProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PenttinenPointProcess.html.
APA
Wolfram Language. (2020). PenttinenPointProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PenttinenPointProcess.html
BibTeX
@misc{reference.wolfram_2025_penttinenpointprocess, author="Wolfram Research", title="{PenttinenPointProcess}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PenttinenPointProcess.html}", note=[Accessed: 14-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_penttinenpointprocess, organization={Wolfram Research}, title={PenttinenPointProcess}, year={2020}, url={https://reference.wolfram.com/language/ref/PenttinenPointProcess.html}, note=[Accessed: 14-August-2025]}