WOLFRAM

Wolfram Language & System Documentation Center

MeanPointDensity[pdata]

estimates the mean point density from point data pdata in the observation region reg.

MeanPointDensity[bdata]

estimates the mean point density from binned data bdata.

MeanPointDensity[pproc]

computes the mean point density for point process pproc.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Related Guides
History
Cite this Page

MeanPointDensity

MeanPointDensity[pdata]

estimates the mean point density from point data pdata in the observation region reg.

MeanPointDensity[bdata]

estimates the mean point density from binned data bdata.

MeanPointDensity[pproc]

computes the mean point density for point process pproc.

Details and Options

  • MeanPointDensity is also known as intensity or mean intensity.
  • The mean point density is the average number of points per unit measure of the observation region. It is given by , where is the number of points and is the measure of the observation region reg.
  • The points 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.
  • The point process pproc can have the following forms:
  • proca point process proc
    {proc,reg}a point process proc and observation region reg
  • The observation region reg should be a parameter-free, full-dimensional and bounded region as tested by SpatialObservationRegionQ.
  • The binned data bdata is taken to come from SpatialBinnedPointData.
  • With a point process pproc, either exact formulas or approximate computation methods are used.

Examples

open all close all

Basic Examples  (4)

Find the mean point density of cities in California:

Wolfram Language code: cities = CityData[{All, "California"}];
Wolfram Language code: GeoListPlot[cities]
Wolfram Language code: MeanPointDensity[{cities, Entity["AdministrativeDivision", {"California", "UnitedStates"}]}]//N

Create a SpatialPointData:

Wolfram Language code: spd = SpatialPointData[RandomReal[1, {300, 2}]]

Plot the points:

Wolfram Language code: PointValuePlot[spd]

Mean point density:

Wolfram Language code: MeanPointDensity[spd]

Mean point density of a point process:

Wolfram Language code: MeanPointDensity[PoissonPointProcess[30, 2]]
Wolfram Language code: MeanPointDensity[ThomasPointProcess[30, 12, 3, 2]]

Mean point density of a point process on the surface of the Earth:

Wolfram Language code: proc = HardcorePointProcess[Quantity[0.001, 1/"Kilometers"^2], Quantity[30, "Kilometers"], 2]; reg = GeoBoundsRegion[{{0, 1}, {0, 1}}];
Wolfram Language code: MeanPointDensity[{proc, reg}]

Scope  (2)

Mean point density of points in 2D:

Wolfram Language code: pts = RandomPoint[Disk[], 100];
Wolfram Language code: MeanPointDensity[pts]

Specify points and the original region:

Wolfram Language code: reg1 = Disk[];
Wolfram Language code: Graphics[{Opacity[.2], reg1, Opacity[1], Point[pts]}, Axes -> True]
Wolfram Language code: MeanPointDensity[{pts, reg1}]

Specify another region:

Wolfram Language code: reg2 = Disk[{1 / 2, 0}, 1];
Wolfram Language code: Graphics[{Opacity[.2], reg2, Opacity[1], Point[pts]}, Axes -> True]
Wolfram Language code: MeanPointDensity[{pts, reg2}]

Estimate mean point density for a hardcore point process:

Wolfram Language code: proc = HardcorePointProcess[20, .3, 2]; reg = Disk[];
Wolfram Language code: MeanPointDensity[{proc, reg}]
Wolfram Language code: N[%]
Wolfram Research (2020), MeanPointDensity, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanPointDensity.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_meanpointdensity, author="Wolfram Research", title="{MeanPointDensity}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MeanPointDensity.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_meanpointdensity, organization={Wolfram Research}, title={MeanPointDensity}, year={2020}, url={https://reference.wolfram.com/language/ref/MeanPointDensity.html}, note=[Accessed: 12-June-2026]}