Sample Data: NZ Trees

Source Notebook

Locations of New Zealand trees without annotations

Details

Locations of New Zealand trees in the observation region Rectangle[{0, 0}, {153, 95}] feet without annotations.

Examples

Basic Examples (1) 

In[1]:=
ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"]
Out[1]=

Summary of the spatial point data:

In[2]:=
ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"]["Summary"]
Out[2]=

Visualizations (2) 

Plot the spatial point data:

In[3]:=
ListPlot[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"]]
Out[3]=

Visualize smooth point density of the data:

In[4]:=
density = SmoothPointDensity[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"]]
Out[4]=
In[5]:=
Show[ContourPlot[density[{x, y}], {x, y} \[Element] ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "ObservationRegion"], ColorFunction -> "Rainbow"], ListPlot[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"], PlotStyle -> Black]]
Out[5]=

Analysis (6) 

Compute probability of finding a point within given radius of an existing point - NearestNeighborG is the CDF of the nearest neighbor distribution:

In[6]:=
nnG = NearestNeighborG[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"]]
Out[6]=
In[7]:=
maxR = N[nnG["MaxRadius"]]
Out[7]=
In[8]:=
DiscretePlot[nnG[r], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
Out[8]=

NearestNeighborG as the CDF of nearest neighbor distribution can be used to compute the mean distance between a typical point and its nearest neighbor - the mean of a positive support distribution can be approximated via a Riemann sum of 1- CDF. To use Riemann approximation create the partition of the support interval from 0 to maxR into 100 parts and compute the value of the NearestNeighborG at the middle of each subinterval:

In[9]:=
step = maxR/100;
middles = Subdivide[step/2, maxR - step/2, 99];
values = nnG[middles];

Now compute the Riemann sum to find the mean distance between a typical point and its nearest neighbor:

In[10]:=
Total[(1 - values)*step]
Out[10]=

Account for scale and units:

In[11]:=
 %*ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "RegionScale"]
Out[11]=

Test for complete spacial randomness:

In[12]:=
SpatialRandomnessTest[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"], {"PValue", "TestConclusion"}] // Column
Out[12]=

Fit a Poisson point process to the data:

In[13]:=
EstimatedPointProcess[ResourceData[\!\(\*
TagBox["\"\<Sample Data: NZ Trees\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: NZ Trees-Input",
AutoDelete->True]\), "Data"], PoissonPointProcess[\[Mu], 2]]
Out[13]=

Gosia Konwerska, "Sample Data: NZ Trees" from the Wolfram Data Repository (2022)  

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