BUILT-IN MATHEMATICA SYMBOL

SmoothHistogram3D

plots a 3D smooth kernel histogram of the values

.

SmoothHistogram3D

plots a 3D smooth kernel histogram with estimator specification espec.

SmoothHistogram3D

plots the distribution function dfun.

SmoothHistogram3D

plots smooth kernel histograms for multiple datasets

.

MORE INFORMATION

SmoothHistogram3D[data] by default plots the PDF of , based on a smooth kernel density estimate.

The estimator specification espec can be of the form bw or .

The specification for bandwidth bw and kernel are the same as for SmoothKernelDistribution.

Possible distribution functions dfun include:

	"PDF"	probability density function
	"CDF"	cumulative distribution function
	"SF"	survival function
	"HF"	hazard function
	"CHF"	cumulative hazard function

The form provides a wrapper w to be applied to the resulting graphics primitives.

The following wrappers can be used:

	Annotation[e,label]	provide an annotation
	Button[e,action]	define an action to execute when the element is clicked
	EventHandler[e,...]	define a general event handler for the element
	Hyperlink[e,uri]	make the element act as a hyperlink
	PopupWindow[e,cont]	attach a popup window to the element
	StatusArea[e,label]	display in the status area when the element is moused over
	Style[e,opts]	show the element using the specified styles
	Tooltip[e,label]	attach an arbitrary tooltip to the element

SmoothHistogram3D has the same options as Graphics3D with the following additions and changes:

Axes	True	whether to draw axes
BoundaryStyle	Automatic	how to draw boundary lines for surfaces
BoxRatios	{1,1,0.4}	bounding 3D box ratios
ClippingStyle	Automatic	how to draw clipped parts of surfaces
ColorFunction	Automatic	how to determine the color of surfaces
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
Filling	None	filling under each surface
FillingStyle	Opacity[0.5]	style to use for filling
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
Mesh	Automatic	how many mesh lines in each direction to draw
MeshFunctions	{#3&}	how to determine the placement of mesh lines
MeshShading	None	how to shade regions between mesh lines
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for refining surfaces
NormalsFunction	Automatic	how to determine effective surface normals
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	the initial number of sample points in each direction
PlotRange	Automatic	the range of z or other values to include
PlotStyle	Automatic	graphics directives for the style for each surface
RegionFunction	(True&)	how to determine whether a point should be included
ScalingFunctions	None	how to scale individual coordinates
WorkingPrecision	MachinePrecision	the precision used in internal computations

The arguments supplied to RegionFunction, MeshFunctions, NormalsFunction, and ColorFunction are x, y, and f, where f can be the PDF, CDF, etc. of the distribution.

With ScalingFunctions, the coordinate is scaled using , the coordinate is scaled using , and the coordinate is scaled using .

EXAMPLES

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Basic Examples (3)

Plot a smooth density function for a dataset:

Plot several datasets:

Plot the probability density function of the data:

Cumulative distribution function:

Survival function:

Hazard function:

Cumulative hazard function:

Plot a smooth density function for a dataset:

In[1]:=

Out[1]=

Plot several datasets:

In[1]:=

Out[1]=

Plot the probability density function of the data:

In[1]:=

In[2]:=

Out[2]=

Cumulative distribution function:

In[3]:=

Out[3]=

Survival function:

In[4]:=

Out[4]=

Hazard function:

In[5]:=

Out[5]=

Cumulative hazard function:

In[6]:=

Out[6]=

Scope (23)

Plot different distribution functions:

PlotRange is selected automatically:

Use PlotRange to focus on areas of interest:

Non-real data points are ignored:

Specify the number of points to use:

Specify the number of times to refine the surface:

Use wrappers on datasets:

Use the default tooltip for the data:

Override the default tooltips:

Specify a single bandwidth for bivariate data:

Specify bivariate bandwidths in units of standard deviation:

Allow bivariate bandwidths to vary adaptively with local density:

Use the local sensitivity from 0.25 (small) to 0.75 (large):

Vary the initial bandwidth for an adaptive estimate:

Use initial bandwidths of 1. and 0.25:

Use any of several automatic bandwidth selection methods:

Silverman's method is used by default for bandwidth selection:

The PDFs are equivalent:

Use different bandwidth specifications in each dimension:

Specify any one of several kernel functions:

Define the kernel function as a pure function:

Provide an explicit PlotStyle for the surface:

Use neutral lighting:

Provide separate styles for different surfaces:

Add labels:

Color the surface by height:

Style the areas between mesh lines:

Create an overlay mesh:

Options (59)

Use a black boundary around the edges of the surface:

Do not use any boundary:

Use a thick boundary around the edges of the surface:

BoundaryStyle applies to holes cut by RegionFunction:

Automatic uses the natural scale from PlotRange:

Use BoxRatios to emphasize some particular feature, in this case the peaks of the surface:

Color clipped regions like the rest of the surface:

Do not draw clipped regions:

Make clipped regions partially transparent:

Color clipped regions red at the bottom and blue at the top:

Color by scaled

,

, and

values:

Color according to the

and

coordinates:

Color by scaled

coordinate:

Named color gradients from ColorData color in the

direction:

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

Use unscaled coordinates:

Use scaled coordinates in the

and

directions and unscaled coordinates in the

direction:

Fill to the top:

Filling occurs along the region cut by the RegionFunction:

Fill to both top and bottom:

Fill to the bottom with a variety of styles:

Fill to the plane

with red below:

Colored lights are used to shade the surface:

Lighting

uses white lights:

Refine the surface where it changes quickly:

SmoothHistogram3D typically has 10 mesh lines in the

direction:

Use 5 mesh lines in the

direction:

Use no mesh:

Show the complete sampling mesh:

Use 3 mesh lines in the

direction and 6 mesh lines in the

direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

SmoothHistogram3D uses a height mesh by default:

Use mesh lines in the

and

directions:

Use mesh lines corresponding to fixed distances from the mean:

Use None to remove regions:

Lay a checkerboard pattern over a surface:

MeshShading has a higher priority than PlotStyle:

MeshShading has a higher priority than ColorFunction:

Use red mesh lines:

Use red mesh lines in the

direction and thick mesh lines in the

direction:

Normals are automatically calculated:

Use None to get flat shading for all the polygons:

Vary the effective normals used on the surface:

Use more initial points to get a smoother surface:

Use 20 initial points in the

direction and 5 in the

direction:

SmoothHistogram3D automatically selects the domain:

Use the full domain generated by SmoothKernelDistribution:

Explicitly provide the domain:

Show the surface over the full

,

range from the data:

Use an explicit

range to emphasize features:

Color a surface with diffuse orange:

Use Specularity to get highlights:

Use Opacity to get transparent surfaces:

Use separate styles for each of the surfaces:

Produce a wire mesh:

Clip small values of the surface:

Filling will fill from the region boundary:

Regions do not have to be connected:

Use any logical combination of conditions:

Applications (2)

Determine the number of modes present in bivariate data. It is good practice to observe the density over a range of bandwidths:

Over several bandwidth choices two modes are identified:

Compare the distribution of data to a parametric model:

Quantify the comparison with DistributionFitTest:

Properties & Relations (7)

SmoothHistogram3D effectively plots the distribution function of SmoothKernelDistribution:

Use SmoothDensityHistogram and SmoothHistogram3D for bivariate data:

Use SmoothHistogram for univariate data:

Use Histogram3D and DensityHistogram to plot the data in discrete bins:

Use DiscretePlot3D to plot the data at discrete points:

Additional points will result in a better approximation of the underlying distribution:

As the bandwidth approaches infinity, the estimate approaches the shape of the kernel:

Neat Examples (1)

Visualize the density of Old Faithful geyser data with the original data as an inset graphic: