# RandomPointConfiguration

RandomPointConfiguration[pproc,reg]

generates a pseudorandom spatial point configuration from the spatial point process pproc in the observation region reg.

RandomPointConfiguration[pproc,reg, n]

generates an ensemble of n spatial point configurations.

# Details and Options

• RandomPointConfiguration takes a point process pproc and generates a point configuration as a SpatialPointData object.
•
• RandomPointConfiguration gives a different realization of pseudorandom point configurations whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.
• The same process can generate an ensemble consisting of different realizations.
•
• The observation region reg needs to be a parameter-free region, as well as SpatialObservationRegionQ.
• The following options can be given:
•  Method Automatic what method to use WorkingPrecision MachinePrecision precision used in internal computations
• With the setting , random numbers of precision p will be generated.
• Special settings for Method are documented under the individual point process reference pages.
• Typical Method settings include:
•  "MCMC" Markov chain Monte Carlo birth and death "Thinning" random thinning "Exact" coupling from the past

# Examples

open allclose all

## Basic Examples(2)

Sample from a Poisson point process:

Sample 5 realizations from a binomial point process:

## Scope(5)

RandomPointConfiguration returns a SpatialPointData object:

Obtain a list of locations of the points:

Simulate a Strauss point process in a rectangle:

Retrieve points that lie within a unit disk centered at {2,3}:

Visualize points on the plane:

Estimate the parameters for a point process using a simulated point configuration:

Simulate from a Cauchy point process:

Estimate Ripley's function from the sampled point configuration and compare it with the theoretical function:

Simulate an ensemble of 5 realizations over the same region:

Number of points in each realization:

Visualize the distribution of points in different realizations:

## Options(3)

### Method(2)

Sample from an InhomogeneousPoissonPointProcess using the different methods:

Use the method "Thinning":

Use the Markov chain Monte Carlo method "MCMC":

Visualize samples over the region:

Sample from a Gibbs point process using the Markov chain Monte Carlo method "MCMC" with the number of iterations equal to 30000:

### WorkingPrecision(1)

Generate a sample point configuration with default machine precision:

Use WorkingPrecision to generate a sample point configuration with higher precision:

## Applications(2)

Estimate the density of a PoissonPointProcess from a sample:

The intensity estimate:

Compare the expected point counts and the average of number of points for an inhomogeneous Poisson point process:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_randompointconfiguration, author="Wolfram Research", title="{RandomPointConfiguration}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}", note=[Accessed: 20-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_randompointconfiguration, organization={Wolfram Research}, title={RandomPointConfiguration}, year={2020}, url={https://reference.wolfram.com/language/ref/RandomPointConfiguration.html}, note=[Accessed: 20-April-2024 ]}