PointProcessFitTest
✖
PointProcessFitTest
tests whether the point collection pdata could be modeled by a Poisson point process.
tests whether the point collection could be modeled by the point process pproc.
Details and Options



- PointProcessFitTest performs a goodness-of-fit hypothesis test with null hypothesis
that pdata was drawn from a point process pproc and alternative hypothesis
that it was not.
- By default, a probability value or
-value is returned.
- A small
-value suggests that it is unlikely that pdata comes from a pproc.
- The point data pdata can have the following forms:
-
{p1,p2,…} points pi GeoPosition[…],GeoPositionXYZ[…],… geographic points SpatialPointData[…] spatial point collection {pts,reg} point collection pts and observation region reg - If the observation region reg is not given, a region is automatically computed using RipleyRassonRegion.
- Under the null hypothesis
, the points in pdata were drawn from pproc. In particular, this means they should have the same BesagL function.
- The following tests can used:
-
"BesagL" computes BesagL on simulations of pproc and pdata "ChiSquare" based on binning, where standard bin count residuals are expected to be chi-square distributed, fast and approximate "ModifiedChiSquare" - based on binning, where counts are expected to be multinomially distributed, exact for small samples, using "ChiSquare" for large data
- PointProcessFitTest[data,proc,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- PointProcessFitTest[data,pproc,"property"] can be used to directly give the value of "property".
- Properties related to the reporting of test results include:
-
"AllTests" list of all applicable tests "AutomaticTest" test chosen if Automatic is used "PValue" list of -values
"PValueTable" formatted table of -values
"ShortTestConclusion" a short description of the conclusion of a test "TestConclusion" a description of the conclusion of a test "TestData" list of pairs of test statistics and -values
"TestDataTable" formatted table of -values and test statistics
"TestStatistic" list of test statistics "TestStatisticTable" formatted table of test statistics - The following options can be used:
-
SignificanceLevel 0.05 cutoff for diagnostics and reporting Method Automatic BesagL method takes suboptions
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Uniform point distribution on a disk:

https://wolfram.com/xid/0ixegh0w74egali-70mhbz

https://wolfram.com/xid/0ixegh0w74egali-eukx3c

The data came from a point process with homogeneous intensity:

https://wolfram.com/xid/0ixegh0w74egali-mammqr

Points distributed over a geographical region:

https://wolfram.com/xid/0ixegh0w74egali-p8dooe

https://wolfram.com/xid/0ixegh0w74egali-qfydy8

Estimated PoissonPointProcess:

https://wolfram.com/xid/0ixegh0w74egali-93k3m


https://wolfram.com/xid/0ixegh0w74egali-h0ash8

Scope (10)Survey of the scope of standard use cases
Testing (7)

https://wolfram.com/xid/0ixegh0w74egali-i89sl7

https://wolfram.com/xid/0ixegh0w74egali-lbx6c9

The -values are typically large when points are uniformly distributed:

https://wolfram.com/xid/0ixegh0w74egali-6x61e

The -values are typically small when there is spatial heterogeneity:

https://wolfram.com/xid/0ixegh0w74egali-ceov9d

Perform a particular test for spatial randomness:

https://wolfram.com/xid/0ixegh0w74egali-by7lps

https://wolfram.com/xid/0ixegh0w74egali-bvmrdn

Using Automatic applies the "BesagL" test:

https://wolfram.com/xid/0ixegh0w74egali-ee4ai7

https://wolfram.com/xid/0ixegh0w74egali-bid6jg

The property "AutomaticTest" can be used to determine which test was chosen:

https://wolfram.com/xid/0ixegh0w74egali-ciuhxp

Perform all tests appropriate to the data simultaneously:

https://wolfram.com/xid/0ixegh0w74egali-d2o4qo

https://wolfram.com/xid/0ixegh0w74egali-0swcog

Use the property "AllTests" to see which tests are available:

https://wolfram.com/xid/0ixegh0w74egali-gvjord

Create a HypothesisTestData object for repeated property extraction:

https://wolfram.com/xid/0ixegh0w74egali-me44um

https://wolfram.com/xid/0ixegh0w74egali-cc8eh1

The properties available for extraction:

https://wolfram.com/xid/0ixegh0w74egali-frvg20

Extract some properties from the HypothesisTestData object:

https://wolfram.com/xid/0ixegh0w74egali-kv96cm

https://wolfram.com/xid/0ixegh0w74egali-bpn9dr
The -value and test statistic from the "BesagL" test:

https://wolfram.com/xid/0ixegh0w74egali-365dq


https://wolfram.com/xid/0ixegh0w74egali-bn5rjv

Extract any number of properties simultaneously:

https://wolfram.com/xid/0ixegh0w74egali-nm6fad

https://wolfram.com/xid/0ixegh0w74egali-dmu6hk
The -value and test statistic from a "BesagL" test:

https://wolfram.com/xid/0ixegh0w74egali-i6fwj7

Reporting (3)
Tabulate the results from a selection of tests:

https://wolfram.com/xid/0ixegh0w74egali-o6sf7r

https://wolfram.com/xid/0ixegh0w74egali-hb1mu5
A full table of all appropriate test results:

https://wolfram.com/xid/0ixegh0w74egali-c83kyd

A table of selected test results:

https://wolfram.com/xid/0ixegh0w74egali-gxraq6

Retrieve the entries from a test table for customized reporting:

https://wolfram.com/xid/0ixegh0w74egali-ty7cdy

https://wolfram.com/xid/0ixegh0w74egali-98x7a

https://wolfram.com/xid/0ixegh0w74egali-fq0ubv

https://wolfram.com/xid/0ixegh0w74egali-72dsk

The -values are above 0.05, so there is not enough evidence to reject
at that level:

https://wolfram.com/xid/0ixegh0w74egali-evyuso

Tabulate -values for a test or group of tests:

https://wolfram.com/xid/0ixegh0w74egali-72zjtc

https://wolfram.com/xid/0ixegh0w74egali-blo8x

https://wolfram.com/xid/0ixegh0w74egali-g8i1dt


https://wolfram.com/xid/0ixegh0w74egali-o0wuj

A table of -values from all appropriate tests:

https://wolfram.com/xid/0ixegh0w74egali-d225dd

Options (2)Common values & functionality for each option
SignificanceLevel (1)
The significance level is used for "TestConclusion" and "ShortTestConclusion":

https://wolfram.com/xid/0ixegh0w74egali-bhkod7

https://wolfram.com/xid/0ixegh0w74egali-lasldz

https://wolfram.com/xid/0ixegh0w74egali-kfj6j
The test conclusions may differ:

https://wolfram.com/xid/0ixegh0w74egali-nqxmau


https://wolfram.com/xid/0ixegh0w74egali-wyh2kj


https://wolfram.com/xid/0ixegh0w74egali-hpqqgh

MaxIterations (1)
You can control the number of simulations with suboption MaxIterations:

https://wolfram.com/xid/0ixegh0w74egali-mv1su

https://wolfram.com/xid/0ixegh0w74egali-carbz0


https://wolfram.com/xid/0ixegh0w74egali-ineym4

Properties & Relations (1)Properties of the function, and connections to other functions
PointProcessFitTest can be used to test equivalence of complete spatial randomness:

https://wolfram.com/xid/0ixegh0w74egali-duemn2

https://wolfram.com/xid/0ixegh0w74egali-nneev2

SpatialRandomnessTest has built-in, more specific tests:

https://wolfram.com/xid/0ixegh0w74egali-p2th6x


https://wolfram.com/xid/0ixegh0w74egali-e6wds1

Wolfram Research (2020), PointProcessFitTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PointProcessFitTest.html.
Text
Wolfram Research (2020), PointProcessFitTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PointProcessFitTest.html.
Wolfram Research (2020), PointProcessFitTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PointProcessFitTest.html.
CMS
Wolfram Language. 2020. "PointProcessFitTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PointProcessFitTest.html.
Wolfram Language. 2020. "PointProcessFitTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PointProcessFitTest.html.
APA
Wolfram Language. (2020). PointProcessFitTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PointProcessFitTest.html
Wolfram Language. (2020). PointProcessFitTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PointProcessFitTest.html
BibTeX
@misc{reference.wolfram_2025_pointprocessfittest, author="Wolfram Research", title="{PointProcessFitTest}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PointProcessFitTest.html}", note=[Accessed: 08-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_pointprocessfittest, organization={Wolfram Research}, title={PointProcessFitTest}, year={2020}, url={https://reference.wolfram.com/language/ref/PointProcessFitTest.html}, note=[Accessed: 08-July-2025
]}