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SmoothHistogram [{x1,x2,}]

plots a smooth kernel histogram for the PDF of the values xi.

SmoothHistogram [{x1,x2,},espec]

plots a smooth kernel histogram with estimator specification espec.

SmoothHistogram [{x1,x2,},espec,dfun]

plots the distribution function dfun.

SmoothHistogram [{data1,data2,},]

plots smooth kernel histograms for multiple datasets datai.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Tabular Data  
Bandwidth and Kernel  
Presentation  
Options  
AspectRatio  
Axes  
AxesLabel  
Show More Show More
AxesOrigin  
AxesStyle  
ClippingStyle  
ColorFunction  
ColorFunctionScaling  
Filling  
FillingStyle  
ImageSize  
MaxRecursion  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
PerformanceGoal  
PlotLayout  
PlotPoints  
PlotRange  
PlotStyle  
PlotTheme  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Related Guides
Related Links
History
Cite this Page

SmoothHistogram [{x1,x2,}]

plots a smooth kernel histogram for the PDF of the values xi.

SmoothHistogram [{x1,x2,},espec]

plots a smooth kernel histogram with estimator specification espec.

SmoothHistogram [{x1,x2,},espec,dfun]

plots the distribution function dfun.

SmoothHistogram [{data1,data2,},]

plots smooth kernel histograms for multiple datasets datai.

Details and Options

Examples

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Basic Examples  (3)

Plot a dataset:

Plot several datasets:

Plot the probability density function of the data:

Cumulative distribution function:

Survival function:

Hazard function:

Cumulative hazard function:

Scope  (30)

Data  (11)

Plot multiple datasets:

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 times to refine the curve:

Use wrappers on datasets:

Override the default tooltips:

Use any object in the tooltip:

Use PopupWindow to provide additional drilldown information:

Numeric values in an association are used as the y coordinates:

Numeric keys and values in an association are used as the x and y coordinates:

Plot time series directly:

The weights in WeightedData are ignored:

Tabular Data  (1)

Get tabular data:

Create a smooth histogram for the city mileage:

Compare the distributions of city and highway mileages:

Vary the bandwidth to affect the smoothness of the histograms:

Bandwidth and Kernel  (9)

Automatically select the bandwidth to use:

More data yields better approximations to the underlying distribution:

Explicitly specify the bandwidth:

Larger bandwidths yield smoother estimates:

Specify bandwidths in units of standard deviation:

Use bandwidths of and of the standard deviation:

Allow bandwidth to vary adaptively with local density:

Vary the local sensitivity from (none) to (full):

Vary the initial bandwidth for an adaptive estimate:

Specify an initial bandwidth of and respectively:

Use any of several automatic bandwidth selection methods:

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

The PDFs are equivalent:

Specify any one of several kernel functions:

Define the kernel function as a pure function:

Presentation  (9)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Use rows and columns of individual plots to show multiple sets:

Add labels:

Use the default tooltip for the data:

Provide an interactive tooltip for the data:

Create filled plots:

Create an overlay mesh:

Style the curve segments between mesh points:

Options  (79)

AspectRatio  (4)

By default, SmoothHistogram uses a fixed height to width ratio for the plot:

Make the height the same as the width with AspectRatio 1:

AspectRatio Automatic determines the ratio from the plot ranges:

AspectRatio Full adjusts the height and width to tightly fit inside other constructs:

Axes  (4)

By default, axes are drawn:

Use Axes False to turn off axes:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

AxesLabel  (4)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

Use units as labels:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

ClippingStyle  (4)

Omit clipped regions of the plot:

Show the clipped regions like the rest of the curve:

Show the clipped regions with red lines:

Show the clipped regions as red and thick:

ColorFunction  (5)

Color by scaled and coordinates:

Color with a named color scheme:

Fill with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use Automatic in MeshShading to use ColorFunction :

ColorFunctionScaling  (2)

Color the line based on scaled value:

Color the line based on unscaled value:

Filling  (6)

Use symbolic or explicit values:

By default, overlapping fills combine using opacity:

Fill between curve 1 and the axis:

Fill between curves 1 and 2:

Fill between datasets using a particular style:

Use different styles above and below the filling level:

FillingStyle  (4)

Use different fill colors:

Fill with opacity 0.5 orange:

Fill with red when the first curve is below the second, and blue when the second is below the first:

Use a variable filling style obtained from a ColorFunction :

ImageSize  (7)

Use named sizes such as Tiny , Small , Medium and Large :

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatio Full will fill the available space:

Use maximum sizes for the width and height:

Use ImageSize Full to fill the available space in an object:

Specify the image size as a fraction of the available space:

MaxRecursion  (2)

The default sampling mesh:

Each level of MaxRecursion will subdivide the initial mesh into a finer mesh:

Mesh  (3)

Use 20 mesh levels evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

Specify and mesh levels and styles in the direction:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show five mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

Alternate red and blue segments of equal width in the direction:

Use None to remove segments:

MeshShading can be used with PlotStyle :

MeshShading has higher priority than PlotStyle for styling the curve:

Use PlotStyle for some segments by setting MeshShading to Automatic :

MeshShading can be used with ColorFunction :

MeshStyle  (4)

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big, red mesh points in the direction:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLayout  (3)

Place each histogram in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

PlotPoints  (1)

Use more initial points to get a smoother curve:

PlotRange  (2)

PlotRange is automatically calculated:

Show the full range:

SmoothHistogram automatically chooses the plotting domain:

Plot over the middle 90% of the data:

PlotStyle  (6)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotStyle can be combined with ColorFunction :

PlotStyle can be combined with MeshShading :

MeshStyle by default uses the same style as PlotStyle :

PlotTheme  (2)

Use a theme with simple ticks and grid lines in a high contrast color scheme:

Change the color scheme:

Applications  (4)

The velocities in km/sec of 82 galaxies from six well-separated conic sections of an unfilled survey of the Corona Borealis region. Multimodality in such surveys is evidence for voids and superclusters in the far universe:

Multiple modes are readily detected for a variety of bandwidths:

Observe the density over many possible bandwidths and choose one that captures important features of the data while smoothing out noise. For presentation, it is best to choose a bandwidth that slightly undersmooths the data:

Choosing 6.0 seems to capture the important features of the snowfall data:

Visually compare data to a parametric model of its density:

Smooth histogram for the slice distribution of a random process:

Smooth histogram for several slices of a process:

Properties & Relations  (5)

SmoothHistogram effectively plots the distribution function of SmoothKernelDistribution :

Use Histogram to plot the data in discrete bins:

Use SmoothDensityHistogram and SmoothHistogram3D for bivariate data:

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:

Possible Issues  (1)

Using SmoothHistogram with multivariate data will plot multiple curves:

Neat Examples  (1)

A visual explanation of kernel density estimation:

The estimate results from mixing the kernel functions placed at each data point:

Wolfram Research (2010), SmoothHistogram, Wolfram Language function, https://reference.wolfram.com/language/ref/SmoothHistogram.html (updated 2025).

Text

Wolfram Research (2010), SmoothHistogram, Wolfram Language function, https://reference.wolfram.com/language/ref/SmoothHistogram.html (updated 2025).

CMS

Wolfram Language. 2010. "SmoothHistogram." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/SmoothHistogram.html.

APA

Wolfram Language. (2010). SmoothHistogram. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SmoothHistogram.html

BibTeX

@misc{reference.wolfram_2025_smoothhistogram, author="Wolfram Research", title="{SmoothHistogram}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/SmoothHistogram.html}", note=[Accessed: 16-November-2025]}

BibLaTeX

@online{reference.wolfram_2025_smoothhistogram, organization={Wolfram Research}, title={SmoothHistogram}, year={2025}, url={https://reference.wolfram.com/language/ref/SmoothHistogram.html}, note=[Accessed: 16-November-2025]}

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