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Wolfram Language & System Documentation Center
ProbabilityPlot
  • See Also
    • QuantilePlot
    • ProbabilityScalePlot
    • Quantile
    • Histogram
    • BoxWhiskerChart
    • DistributionChart
    • ListPlot
    • DiscretePlot
    • Plot
  • Related Guides
    • Statistical Visualization
    • Random Variables
    • Reliability
    • See Also
      • QuantilePlot
      • ProbabilityScalePlot
      • Quantile
      • Histogram
      • BoxWhiskerChart
      • DistributionChart
      • ListPlot
      • DiscretePlot
      • Plot
    • Related Guides
      • Statistical Visualization
      • Random Variables
      • Reliability

ProbabilityPlot[list]

generates a plot of the CDF of list against the CDF of a normal distribution.

ProbabilityPlot[dist]

generates a plot of the CDF of the distribution dist against the CDF of a normal distribution.

ProbabilityPlot[data,rdata]

generates a plot of the CDF of data against the CDF of rdata.

ProbabilityPlot[data,rdist]

generates a plot of the CDF of data against the CDF of symbolic distribution rdist.

ProbabilityPlot[{data1,data2,…},ref]

generates a plot of the CDF of datai against the CDF of a reference distribution ref.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data and Distributions  
Tabular Data  
Presentation  
Options  
ColorFunction  
ColorFunctionScaling  
Filling  
Show More Show More
FillingStyle  
Joined  
Mesh  
MeshFunctions  
MeshShading  
MeshStyle  
PlotHighlighting  
PlotLegends  
PlotMarkers  
PlotStyle  
PlotTheme  
ReferenceLineStyle  
ScalingFunctions  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • QuantilePlot
    • ProbabilityScalePlot
    • Quantile
    • Histogram
    • BoxWhiskerChart
    • DistributionChart
    • ListPlot
    • DiscretePlot
    • Plot
  • Related Guides
    • Statistical Visualization
    • Random Variables
    • Reliability
    • See Also
      • QuantilePlot
      • ProbabilityScalePlot
      • Quantile
      • Histogram
      • BoxWhiskerChart
      • DistributionChart
      • ListPlot
      • DiscretePlot
      • Plot
    • Related Guides
      • Statistical Visualization
      • Random Variables
      • Reliability

ProbabilityPlot

ProbabilityPlot[list]

generates a plot of the CDF of list against the CDF of a normal distribution.

ProbabilityPlot[dist]

generates a plot of the CDF of the distribution dist against the CDF of a normal distribution.

ProbabilityPlot[data,rdata]

generates a plot of the CDF of data against the CDF of rdata.

ProbabilityPlot[data,rdist]

generates a plot of the CDF of data against the CDF of symbolic distribution rdist.

ProbabilityPlot[{data1,data2,…},ref]

generates a plot of the CDF of datai against the CDF of a reference distribution ref.

Details and Options

  • ProbabilityPlot is also known as normal probability plot in the one-argument form and probability-probability (P-P) plot in the two-argument form.
  • ProbabilityPlot[data1,data2] works with datai being either a dataset of real values or a symbolic univariate distribution.
  • For datasets list, empirical CDFs are used, and for symbolic distributions dist, exact CDFs are used.
  • ProbabilityPlot[data,dist[θ1,…]] with symbolic parameters θi is equivalent to ProbabilityPlot[data,EstimatedDistribution[data,dist[θ1,…]]].
  • Datasets can be given in the following forms:
  • {x1,x2,…}list of samples
    {Quantity[x1,unit],Quantity[x2,unit],…}samples with units
    <|k1e1,k2e2,…|>association of keys and samples
    WeightedData[…],EventData[…]augmented datasets
    TimeSeries[…],EventSeries[…],TemporalData[…]time series, event series, and temporal data
    w[{e1,e2,…},…]wrapper applied to a whole dataset
    w[{data1,data2,…}]wrapper applied to all datasets
  • The form w[data] or w[dist] provides a wrapper w to be applied to the resulting graphics primitives.
  • ProbabilityPlot[Tabular[…]cspec] extracts and plots values from the tabular object using the column specification cspec.
  • The following forms of column specifications cspec are allowed for plotting tabular data:
  • colxplot the values from column x
    {colx1,colx2,…}plot columns x1, x2, …
  • 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
    Highlighted[fi,effect]dynamically highlight fi with an effect
    Highlighted[fi,Placed[effect,pos]]statically highlight fi with an effect at position pos
    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
  • ProbabilityPlot has the same options as Graphics, with the following additions and changes: [List of all options]
  • AspectRatio1/GoldenRatioratio of width to height
    ClippingStyleAutomaticwhat to draw where curves are clipped
    ColorFunction Automatichow to determine the coloring of curves
    ColorFunctionScaling Truewhether to scale arguments to ColorFunction
    Filling Nonefilling to insert under each curve
    FillingStyle Automaticstyle to use for filling
    Joined Automaticwhether to join points
    Mesh Nonehow many mesh points to draw on each curve
    MeshFunctions {#1&}how to determine the placement of mesh points
    MeshShading Nonehow to shade regions between mesh points
    MeshStyle Automaticthe style for mesh points
    MethodAutomaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlighting Automatichighlighting effect for data
    PlotLegends Nonelegends for data points
    PlotMarkers Nonemarkers to use to indicate each point for datasets
    PlotRangeAutomaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyle Automaticgraphics directives to specify the style for each object
    PlotTheme $PlotThemeoverall theme for the plot
    ReferenceLineStyle Automaticstyle for the reference line
    ScalingFunctions Nonehow to scale individual coordinates
    WorkingPrecisionMachinePrecisionthe precision used in internal computations for symbolic distributions
  • With Filling->Automatic, the region between a dataset and reference line will be filled. By default, "stems" are used for datasets, and "solid" filling is used for symbolic distributions. The setting Joined->True will force "solid" filling for datasets.
  • The arguments supplied to functions in MeshFunctions and RegionFunction are , . Functions in ColorFunction are by default supplied with scaled versions of these arguments.
  • The setting Joined->Automatic is equivalent to Joined->True when comparing two distributions and Joined->False otherwise.
  • The setting PlotStyle->Automatic uses a sequence of different plot styles for different lines.
  • ColorData["DefaultPlotColors"] gives the default sequence of colors used by PlotStyle.
  • With the ReferenceLineStyle->None, no reference line will be drawn.
  • Possible highlighting effects for Highlighted and PlotHighlighting include:
  • stylehighlight the indicated curve
    "Ball"highlight and label the indicated point in a curve
    "Dropline"highlight and label the indicated point in a curve with droplines to the axes
    "XSlice"highlight and label all points along a vertical slice
    "YSlice"highlight and label all points along a horizontal slice
    Placed[effect,pos]statically highlight the given position pos
  • Highlight position specifications pos include:
  • x, {x}effect at {x,y} with y chosen automatically
    {x,y}effect at {x,y}
    {pos1,pos2,…}multiple positions posi
  • Typical settings for PlotLegends include:
  • Noneno legend
    Automaticautomatically determine legend
    {lbl1,lbl2,…}use lbl1, lbl2, … as legend labels
    Placed[lspec,…]specify placement for legend
  • With ScalingFunctions->{sx,sy}, the coordinate is scaled using sx and the coordinate is scaled using sy.
  • List of all options
  • Highlight options with settings specific to ProbabilityPlot
  • AlignmentPointCenterthe default point in the graphic to align with
    AspectRatio1/GoldenRatioratio of width to height
    AxesFalsewhether to draw axes
    AxesLabelNoneaxes labels
    AxesOriginAutomaticwhere axes should cross
    AxesStyle{}style specifications for the axes
    BackgroundNonebackground color for the plot
    BaselinePositionAutomatichow to align with a surrounding text baseline
    BaseStyle{}base style specifications for the graphic
    ClippingStyleAutomaticwhat to draw where curves are clipped
    ColorFunctionAutomatichow to determine the coloring of curves
    ColorFunctionScalingTruewhether to scale arguments to ColorFunction
    ContentSelectableAutomaticwhether to allow contents to be selected
    CoordinatesToolOptionsAutomaticdetailed behavior of the coordinates tool
    Epilog{}primitives rendered after the main plot
    FillingNonefilling to insert under each curve
    FillingStyleAutomaticstyle to use for filling
    FormatTypeTraditionalFormthe default format type for text
    FrameFalsewhether to put a frame around the plot
    FrameLabelNoneframe labels
    FrameStyle{}style specifications for the frame
    FrameTicksAutomaticframe ticks
    FrameTicksStyle{}style specifications for frame ticks
    GridLinesNonegrid lines to draw
    GridLinesStyle{}style specifications for grid lines
    ImageMargins0.the margins to leave around the graphic
    ImagePaddingAllwhat extra padding to allow for labels etc.
    ImageSizeAutomaticthe absolute size at which to render the graphic
    JoinedAutomaticwhether to join points
    LabelStyle{}style specifications for labels
    MeshNonehow many mesh points to draw on each curve
    MeshFunctions{#1&}how to determine the placement of mesh points
    MeshShadingNonehow to shade regions between mesh points
    MeshStyleAutomaticthe style for mesh points
    MethodAutomaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlightingAutomatichighlighting effect for data
    PlotLabelNonean overall label for the plot
    PlotLegendsNonelegends for data points
    PlotMarkersNonemarkers to use to indicate each point for datasets
    PlotRangeAutomaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotRangePaddingAutomatichow much to pad the range of values
    PlotRegionAutomaticthe final display region to be filled
    PlotStyleAutomaticgraphics directives to specify the style for each object
    PlotTheme$PlotThemeoverall theme for the plot
    PreserveImageOptionsAutomaticwhether to preserve image options when displaying new versions of the same graphic
    Prolog{}primitives rendered before the main plot
    ReferenceLineStyleAutomaticstyle for the reference line
    RotateLabelTruewhether to rotate y labels on the frame
    ScalingFunctionsNonehow to scale individual coordinates
    TicksAutomaticaxes ticks
    TicksStyle{}style specifications for axes ticks
    WorkingPrecisionMachinePrecisionthe precision used in internal computations for symbolic distributions

Examples

open all close all

Basic Examples  (4)

A normal probability plot compared to an estimated normal distribution:

Compare to the standard normal distribution:

A probability-probability plot of two datasets:

Plot several datasets with a legend:

Scope  (26)

Data and Distributions  (12)

ProbabilityPlot works with numeric data:

ProbabilityPlot works with symbolic distributions:

Use multiple datasets and distributions:

The default reference distribution is the closest estimated NormalDistribution:

Specify data or distributions as the reference:

Reference distributions are estimated for each dataset:

Estimate specific reference distributions for numeric datasets:

Use all forms of built-in distributions:

Parametric:

Nonparametric:

Derived:

Plot values with units:

Plot the values from an association:

Plot data with weights:

Plot data from time series:

Tabular Data  (1)

Get tabular data:

Compare the data to a normal distribution:

Compare multiple sets of data:

Use PivotToColumns to generate columns of "SepalWidth" per species:

Compare probability of sepal width per species:

Use abbreviated names for extended keys when the elements are unique:

Use legends for the plot:

Presentation  (13)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Include legends for each dataset:

Add labels:

Use specific styles for the reference line:

Turn off the reference line:

Provide an interactive Tooltip for the data:

Provide a specific tooltip for the data:

Create filled plots:

Use shapes to distinguish different datasets:

Use Joined to connect datasets with lines:

Use a theme with grid lines:

Data usually has interactive callouts showing the coordinates when you mouse over them:

Including specific wrappers or interactions such as tooltips turns off the interactive features:

Choose from multiple interactive highlighting effects:

Options  (67)

ColorFunction  (6)

ColorFunction requires at least one dataset to be Joined:

Color by scaled and coordinates:

Color with a named color scheme:

Fill to the reference line 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)

Fill from the data to the reference line:

Use symbolic or explicit values for filling:

Points fill with stems:

Curves fill with solid regions:

Fill from the third dataset to the axis:

Fill between datasets using a particular style:

Use different styles above and below the filling level:

FillingStyle  (2)

Use different fill colors:

Use a transparent orange filling:

Joined  (2)

Datasets are not joined by default:

Join the points:

Symbolic distributions are joined by default:

Mesh  (3)

Use 20 mesh levels evenly spaced in the direction:

Use the mesh to divide the curve into deciles:

Specify Style and mesh levels in the direction:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show 5 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:

PlotHighlighting  (8)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

Move the mouse over the curve to highlight it with a ball and label:

Move the mouse over the curve to highlight it with a label and droplines to the axes:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Use a component that shows the points on the dataset closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the dataset closest to the mouse cursor:

Use Callout options to change the appearance of the label:

Combine components to create a custom effect:

PlotLegends  (7)

By default, no legends are used:

Generate a legend using labels:

Generate a legend using placeholders:

Legends use the same styles as the plot:

Use Placed to specify the legend placement:

Place the legend inside the plot:

Use LineLegend to change the legend appearance:

PlotMarkers  (7)

ProbabilityPlot normally uses distinct colors to distinguish different sets of data:

Automatically use colors and shapes to distinguish sets of data:

Use shapes only:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

PlotStyle  (3)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotTheme  (2)

Use a theme with grid lines:

Use a theme with high-contrast colors:

Turn off the grid lines:

ReferenceLineStyle  (4)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

Draw a dotted red reference line:

Draw a solid red reference line:

Use None to turn off the reference line:

ReferenceLineStyle can be combined with PlotStyle:

ScalingFunctions  (2)

Data is normally shown on linear scales:

Plot the data on a log-scaled axis:

Applications  (3)

KolmogorovSmirnovTest can be used to create a measure that quantifies the behavior in ProbabilityPlot. The Kolmogorov–Smirnov test statistic is equivalent to the maximum vertical distance between a point in the plot and the reference line:

The -value is larger when the points are closer to the reference line:

A -test for location assumes that the data was drawn from a NormalDistribution. If this assumption does not hold, a nonparametric test such as a signed-rank test is more appropriate. Suppose one wants to test for a location parameter of zero using the following data:

The plot suggests that the tails of the distribution are quite heavy. A SignedRankTest for location is more appropriate than the TTest:

Compare two time slices for a random process:

Properties & Relations  (8)

With no second argument, data is compared against an estimated normal distribution:

QuantilePlot compares quantiles for the data:

ProbabilityScalePlot scales the axes so that points from distributions are on a straight line:

BoxWhiskerChart and DistributionChart can be used to visualize the distribution of data:

SmoothHistogram and Histogram can be used to visualize the distribution of data:

DiscretePlot can be used to visualize the discrete distributions:

Use ListPlot to see the data:

ProbabilityPlot ignores time stamps when input is a TimeSeries:

See Also

QuantilePlot  ProbabilityScalePlot  Quantile  Histogram  BoxWhiskerChart  DistributionChart  ListPlot  DiscretePlot  Plot

Related Guides

    ▪
  • Statistical Visualization
  • ▪
  • Random Variables
  • ▪
  • Reliability

History

Introduced in 2010 (8.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2023 (13.3) ▪ 2025 (14.2)

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_probabilityplot, author="Wolfram Research", title="{ProbabilityPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ProbabilityPlot.html}", note=[Accessed: 01-May-2026]}

BibLaTeX

@online{reference.wolfram_2025_probabilityplot, organization={Wolfram Research}, title={ProbabilityPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ProbabilityPlot.html}, note=[Accessed: 01-May-2026]}

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