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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.
  • Typical settings for PlotLegends include:
  • Noneno legend
    Automaticautomatically determine legend
    {lbl1,lbl2,…}use lbl1, lbl2, … as legend labels
    Placed[lspec,…]specify placement for legend
  • PlotStylesty specifies the styles to use for each curve. Possible settings include:
  • {sty1,sty2,…}sequence of styles for the datasets
    <|"key"val,…|>styling elements for different levels of data
  • The accepted keys are:
  • "Base"overall style for all the datai
    "Lists"list of styles styi for each datai
  • 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
  • With ScalingFunctions->{sx,sy}, the coordinate is scaled using sx and the coordinate is scaled using sy.
  • List of all options

    • 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

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Basic Examples  (4)

A normal probability plot compared to an estimated normal distribution:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[1, 2], 100]]

Compare to the standard normal distribution:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[1, 2], 100], NormalDistribution[0, 1]]

A probability-probability plot of two datasets:

Wolfram Language code: data1 = RandomVariate[NormalDistribution[2, 3], 100]; data2 = RandomVariate[StudentTDistribution[4, 2, 3], 200];
Wolfram Language code: ProbabilityPlot[data1, data2]

Plot several datasets with a legend:

Wolfram Language code: data1 = RandomVariate[NormalDistribution[2, 3], 100]; data2 = RandomVariate[StudentTDistribution[4, 2, 1], 200];
Wolfram Language code: ProbabilityPlot[{data1, data2}, PlotLegends -> {"normal", "Student t"}]

Scope  (26)

Data and Distributions  (12)

ProbabilityPlot works with numeric data:

Wolfram Language code: ProbabilityPlot[RandomVariate[UniformDistribution[{0, 1}], 100]]

ProbabilityPlot works with symbolic distributions:

Wolfram Language code: ProbabilityPlot[UniformDistribution[{0, 1}]]

Use multiple datasets and distributions:

Wolfram Language code: ProbabilityPlot[{RandomReal[NormalDistribution[], 100], RandomInteger[PoissonDistribution[1], 100], WeibullDistribution[2, 2]}]

The default reference distribution is the closest estimated NormalDistribution:

Wolfram Language code: data = RandomVariate[UniformDistribution[{0, 1}], 100]; ref = EstimatedDistribution[data, NormalDistribution[a, b]];
Wolfram Language code: {ProbabilityPlot[data], ProbabilityPlot[data, ref]}

Specify data or distributions as the reference:

Wolfram Language code: data = RandomVariate[UniformDistribution[{0, 1}], 100];
Wolfram Language code: {ProbabilityPlot[data, RandomVariate[NormalDistribution[0, 1], 100]], ProbabilityPlot[data, NormalDistribution[0, 1]]}

Reference distributions are estimated for each dataset:

Wolfram Language code: data = RandomVariate[UniformDistribution[{0, 1}], 100];
Wolfram Language code: ProbabilityPlot[{data, 2 + data ^ 2}, PlotRange -> All]

Estimate specific reference distributions for numeric datasets:

Wolfram Language code: ProbabilityPlot[RandomVariate[UniformDistribution[{0, 1}], 100], WeibullDistribution[a, b, c]]

Use all forms of built-in distributions:

Wolfram Language code: data = RandomVariate[NormalDistribution[2, 1], 100];

Parametric:

Wolfram Language code: ProbabilityPlot[data, WeibullDistribution[2, 5]]

Nonparametric:

Wolfram Language code: ProbabilityPlot[data, SmoothKernelDistribution[data]]

Derived:

Wolfram Language code: ProbabilityPlot[data, TruncatedDistribution[{1, 4}, ExponentialDistribution[1]]]

Plot values with units:

Wolfram Language code: Short[data = EntityValue[EntityList[EntityClass["Country", "Countries"]], "LifeExpectancy"]]
Wolfram Language code: ProbabilityPlot[data]

Plot the values from an association:

Wolfram Language code: ProbabilityPlot[<|"a" -> 2, "b" -> 3, "c" -> 5, "d" -> 7, "e" -> 11|>]

Plot data with weights:

Wolfram Language code: data = WeightedData[RandomVariate[NormalDistribution[], 100], Abs[RandomVariate[NormalDistribution[], 100]]]
Wolfram Language code: ProbabilityPlot[data]

Plot data from time series:

Wolfram Language code: data = TimeSeries[RandomReal[1, 50], {Automatic, Today}]
Wolfram Language code: ProbabilityPlot[data]

Tabular Data  (1)

Get tabular data:

Wolfram Language code: iris = ResourceData["Sample Tabular Data: Fisher Iris"]

Compare the data to a normal distribution:

Wolfram Language code: ProbabilityPlot[iris -> "SepalWidth"]

Compare multiple sets of data:

Wolfram Language code: ProbabilityPlot[iris -> {"SepalWidth", "PetalWidth"}]

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

Wolfram Language code: pivot = PivotToColumns[iris, "Species" -> "SepalWidth"]

Compare probability of sepal width per species:

Wolfram Language code: ProbabilityPlot[pivot -> {ExtendedKey["SepalWidth", "setosa"], ExtendedKey["SepalWidth", "versicolor"], ExtendedKey["SepalWidth", "virginica"]}]

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

Wolfram Language code: ProbabilityPlot[pivot -> {"setosa", "versicolor", "virginica"}]

Use legends for the plot:

Wolfram Language code: ProbabilityPlot[pivot -> {"setosa", "versicolor", "virginica"}, PlotLegends -> {"setosa", "versicolor", "virginica"}]

Presentation  (13)

Multiple datasets are automatically colored to be distinct:

Wolfram Language code: data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};
Wolfram Language code: ProbabilityPlot[data]

Provide explicit styling to different sets:

Wolfram Language code: data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};
Wolfram Language code: ProbabilityPlot[data, PlotStyle -> {Blue, Red}]

Include legends for each dataset:

Wolfram Language code: data = {RandomVariate[NormalDistribution[], 100], RandomVariate[WeibullDistribution[1, 2], 100]};
Wolfram Language code: ProbabilityPlot[data, PlotLegends -> {"one", "two"}]

Add labels:

Wolfram Language code: ProbabilityPlot[RandomVariate[UniformDistribution[{0, 1}], 100], FrameLabel -> {"Empirical Probabilities", "Theoretical Probabilities"}, PlotLabel -> "P-P Plot", PlotStyle -> Purple]

Use specific styles for the reference line:

Wolfram Language code: ProbabilityPlot[Range[100], ReferenceLineStyle -> Directive[Dashing[{}], Red]]

Turn off the reference line:

Wolfram Language code: ProbabilityPlot[Range[100], ReferenceLineStyle -> None]

Provide an interactive Tooltip for the data:

Wolfram Language code: ProbabilityPlot[Tooltip[RandomVariate[UniformDistribution[{0, 1}], 100]], PlotStyle -> Directive[PointSize[Medium], Orange]]

Provide a specific tooltip for the data:

Wolfram Language code: data = RandomVariate[UniformDistribution[{0, 1}], 100];
Wolfram Language code: ProbabilityPlot[Tooltip[data, BoxWhiskerChart[data]], PlotStyle -> Purple]

Create filled plots:

Wolfram Language code: data1 = RandomReal[NormalDistribution[100, 400], 200]; data2 = RandomReal[UniformDistribution[{5, 400}], 500];
Wolfram Language code: ProbabilityPlot[{data1, data2}, Filling -> {1 -> {2}}, Joined -> True]

Use shapes to distinguish different datasets:

Wolfram Language code: ProbabilityPlot[{{1, 2, 3, 5, 8}, {2, 3, 6, 9, 10}, {4, 5, 7, 10, 12}}, PlotMarkers -> Automatic]

Use Joined to connect datasets with lines:

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, Joined -> True, PlotStyle -> Orange]

Use a theme with grid lines:

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotTheme -> "Detailed"]

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

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}]

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

Wolfram Language code: ProbabilityPlot[Callout[{1, 2, 4, 7, 3, 5, 8, 10, 9}, "hello", .6]]

Choose from multiple interactive highlighting effects:

Wolfram Language code: {ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotHighlighting -> "Dropline"], ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotHighlighting -> "XSlice"]}

Options  (67)

ColorFunction  (6)

ColorFunction requires at least one dataset to be Joined:

Wolfram Language code: {ProbabilityPlot[RandomVariate[NormalDistribution[], 100], ColorFunction -> "Rainbow"], ProbabilityPlot[RandomVariate[NormalDistribution[], 100], ColorFunction -> "Rainbow", Joined -> True]}

Color by scaled and coordinates:

Wolfram Language code: Table[ProbabilityPlot[Range[0, 1, 0.025] ^ 2, Joined -> True, ColorFunction -> Function[{x, y}, f], PlotLabel -> f, PlotStyle -> Thick], {f, {Hue[x], Hue[y]}}]

Color with a named color scheme:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> "DarkRainbow"]

Fill to the reference line with the color used for the curve:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[x]], Filling -> Automatic]

ColorFunction has higher priority than PlotStyle for coloring the curve:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> "DarkRainbow", PlotStyle -> Directive[Red, Thick]]

Use Automatic in MeshShading to use ColorFunction:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[1, 2], 100], Joined -> True, ColorFunction -> "Rainbow", PlotStyle -> Directive[Red, Thick], Mesh -> 9, MeshShading -> {Automatic, StandardGray}, MeshStyle -> None]

ColorFunctionScaling  (2)

Color the line based on scaled value:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[y]], PlotStyle -> Thick, ColorFunctionScaling -> True]

Color the line based on unscaled value:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, ColorFunction -> Function[{x, y}, Hue[y]], PlotStyle -> Thick, ColorFunctionScaling -> False]

Filling  (6)

Fill from the data to the reference line:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], Filling -> Automatic]

Use symbolic or explicit values for filling:

Wolfram Language code: Table[ProbabilityPlot[Range[0, 1, 0.025], Filling -> c], {c, {Top, Bottom, Axis, 0.5}}]

Points fill with stems:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], Filling -> Automatic]

Curves fill with solid regions:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], Filling -> Automatic, Joined -> True]

Fill from the third dataset to the axis:

Wolfram Language code: ProbabilityPlot[{RandomVariate[NormalDistribution[], 14], RandomVariate[PoissonDistribution[1], 10], WeibullDistribution[2, 2]}, Filling -> {3 -> Axis}]

Fill between datasets using a particular style:

Wolfram Language code: ProbabilityPlot[{RandomVariate[WeibullDistribution[1, 2], 100], RandomVariate[WeibullDistribution[2, 4], 100]}, Joined -> True, Filling -> {1 -> {{2}, Directive[Orange, Dashed]}}]

Use different styles above and below the filling level:

Wolfram Language code: ProbabilityPlot[{RandomVariate[WeibullDistribution[1, 2], 100], RandomVariate[WeibullDistribution[2, 4], 100]}, Joined -> True, Filling -> {1 -> {{2}, {Yellow, Red}}}]

FillingStyle  (2)

Use different fill colors:

Wolfram Language code: Table[ProbabilityPlot[Range[0, 1, 0.025], Filling -> Automatic, Joined -> True, FillingStyle -> c], {c, {Red, Green, Blue, Yellow}}]

Use a transparent orange filling:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 3}], Filling -> Bottom, Joined -> True, FillingStyle -> Directive[Opacity[0.3], Orange]]

Joined  (2)

Datasets are not joined by default:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100]]

Join the points:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True]

Symbolic distributions are joined by default:

Wolfram Language code: ProbabilityPlot[LogNormalDistribution[0, 1]]

Mesh  (3)

Use 20 mesh levels evenly spaced in the direction:

Wolfram Language code: ProbabilityPlot[NormalDistribution[], NormalDistribution[], Mesh -> 20]

Use the mesh to divide the curve into deciles:

Wolfram Language code: data = RandomVariate[UniformDistribution[{1, 10}], 100];ProbabilityPlot[data, Joined -> True, Mesh -> {Range[0.1, 0.9, 0.1]}]

Specify Style and mesh levels in the direction:

Wolfram Language code: data = RandomVariate[UniformDistribution[{1, 10}], 100];ProbabilityPlot[data, Joined -> True, Mesh -> {Table[{x, Hue[x]}, {x, 0., 1, .1}]}]

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Wolfram Language code: Table[ProbabilityPlot[Range[0, 1, 0.025], Joined -> True, MeshFunctions -> {Function[{x, y}, Evaluate[f]]}, Mesh -> 9, PlotLabel -> f], {f, {x, y}}]

Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], Joined -> True, Mesh -> {5, 10}, MeshFunctions -> {#1&, #2&}, MeshStyle -> {Directive[PointSize[Medium], Red], Blue}]

MeshShading  (6)

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

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshShading -> {Red, Blue}]

Use None to remove segments:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshShading -> {Red, None}]

MeshShading can be used with PlotStyle:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1&}, MeshShading -> {Red, Blue}]

MeshShading has higher priority than PlotStyle for styling the curve:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> StandardGray, MeshFunctions -> {#1&}, MeshShading -> {Red, Blue}]

Use PlotStyle for some segments by setting MeshShading to Automatic:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Directive[Thick, Yellow], MeshFunctions -> {#1&}, MeshShading -> {Red, Automatic}]

MeshShading can be used with ColorFunction:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, PlotStyle -> Thick, MeshFunctions -> {#1&}, MeshShading -> {StandardGray, Automatic}, ColorFunction -> Function[{x, y}, Hue[x]]]

MeshStyle  (4)

Color the mesh the same color as the plot:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], RandomVariate[NormalDistribution[], 200], Joined -> True, Mesh -> 9, MeshStyle -> Automatic]

Use a red mesh in the direction:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], RandomVariate[NormalDistribution[], 200], Joined -> True, Mesh -> 9, MeshStyle -> Red]

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

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 9, MeshStyle -> {Red, Blue}, MeshFunctions -> {#1&, #2&}]

Use big red mesh points in the direction:

Wolfram Language code: ProbabilityPlot[RandomVariate[NormalDistribution[], 100], Joined -> True, Mesh -> 10, MeshStyle -> Directive[PointSize[Large], Red]]

PlotHighlighting  (8)

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

Wolfram Language code: ProbabilityPlot[{Range[100], RandomVariate[NormalDistribution[2, 3], 100]}]

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

Wolfram Language code: ProbabilityPlot[{Range[100], RandomVariate[NormalDistribution[2, 3], 100]}, PlotHighlighting -> None]

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

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> "Ball"]

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

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> "Dropline"]

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

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> "XSlice"]

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

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> "YSlice"]

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

Wolfram Language code: ProbabilityPlot[{Range[100], RandomVariate[NormalDistribution[2, 3], 100]}, PlotHighlighting -> "XNearestPoint"]

Specify the style for the points:

Wolfram Language code: ProbabilityPlot[{Range[100], RandomVariate[NormalDistribution[2, 3], 100]}, PlotHighlighting -> {"XNearestPoint", <|"Style" -> Red|>}]

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

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> "XYLabel"]

Use Callout options to change the appearance of the label:

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}]

Combine components to create a custom effect:

Wolfram Language code: ProbabilityPlot[Range[100], PlotHighlighting -> {{"XNearestPoint", <|"Style" -> Red|>}, {"XYLabel", <|"Appearance" -> "Corners", "CalloutMarker" -> "Circle"|>}}]

PlotLegends  (7)

By default, no legends are used:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}]

Generate a legend using labels:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> {"sqrt", "log"}]

Generate a legend using placeholders:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> Automatic]

Legends use the same styles as the plot:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotStyle -> {Red, Blue}, PlotLegends -> {"sqrt", "log"}]

Use Placed to specify the legend placement:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> Placed[{"sqrt", "log"}, Below]]

Place the legend inside the plot:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> Placed[{"sqrt", "log"}, {0.25, 0.75}]]

Use LineLegend to change the legend appearance:

Wolfram Language code: ProbabilityPlot[{Sqrt[Range[40]], Log[Range[40]]}, PlotLegends -> LineLegend[{"sqrt", "log"}, LegendFunction -> Frame, LegendMarkers -> None]]

PlotMarkers  (7)

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

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> None]

Automatically use colors and shapes to distinguish sets of data:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> Automatic]

Use shapes only:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> Automatic, PlotStyle -> StandardGray]

Change the size of the default plot markers:

Wolfram Language code: Table[ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> {Automatic, s}], {s, {Tiny, Small, Medium, Large}}]

Use arbitrary text for plot markers:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> {"1", "2", "3", "4"}]

Use explicit graphics for plot markers:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> {[image], [image], [image], [image]}]

Use the same symbol for all the sets of data:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 0.5, 2, 0.5}], PlotMarkers -> {"○"}]

PlotStyle  (3)

Use different style directives:

Wolfram Language code: Table[ProbabilityPlot[Range[0, 1, 0.025], PlotStyle -> ps, Joined -> True], {ps, {Red, Thick, Dashed, Directive[Red, Thick]}}]

By default, different styles are chosen for multiple curves:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 1 / 2, 2, 1 / 2}]]

Explicitly specify the style for different curves:

Wolfram Language code: ProbabilityPlot[Table[Range[0, 1, 0.025] ^ i, {i, 1 / 2, 2, 1 / 2}], PlotStyle -> {Red, Green, Blue, Brown}]

PlotTheme  (2)

Use a theme with grid lines:

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotTheme -> "Detailed"]

Use a theme with high-contrast colors:

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotTheme -> "Marketing"]

Turn off the grid lines:

Wolfram Language code: ProbabilityPlot[{1, 2, 4, 7, 3, 5, 8, 10, 9}, PlotTheme -> "Marketing", GridLines -> None]

ReferenceLineStyle  (4)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025]]

Draw a dotted red reference line:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], ReferenceLineStyle -> Red]

Draw a solid red reference line:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], ReferenceLineStyle -> Directive[Red, Dashing[0]]]

Use None to turn off the reference line:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], ReferenceLineStyle -> None]

ReferenceLineStyle can be combined with PlotStyle:

Wolfram Language code: ProbabilityPlot[Range[0, 1, 0.025], ReferenceLineStyle -> Thick]

ScalingFunctions  (2)

Data is normally shown on linear scales:

Wolfram Language code: ProbabilityPlot[RandomVariate[ExponentialDistribution[4], 100]]

Plot the data on a log-scaled axis:

Wolfram Language code: ProbabilityPlot[RandomVariate[ExponentialDistribution[4], 100], ScalingFunctions -> {None, "Log"}]

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:

Wolfram Language code: data = RandomVariate[𝒟 = ExponentialDistribution[1], 100];
Wolfram Language code: {ProbabilityPlot[data, 𝒟], ProbabilityPlot[data, NormalDistribution[μ, σ]]}

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

Wolfram Language code: {KolmogorovSmirnovTest[data, 𝒟], KolmogorovSmirnovTest[data, NormalDistribution[μ, σ]]}

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:

Wolfram Language code: data = {-6.205, -0.733, 1.304, -4.837, -0.205, -0.382, -0.133, 35.092, -1.128, 6.194, 0.538, -1.197, -4.054, -1.525, -0.318};
Wolfram Language code: ProbabilityPlot[data]

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

Wolfram Language code: SignedRankTest[data, 0, "TestDataTable"]

Compare two time slices for a random process:

Wolfram Language code: data1 = RandomVariate[WienerProcess[0, 2][5], 10 ^ 3]; data2 = RandomVariate[WienerProcess[0, 2][2], 10 ^ 3];
Wolfram Language code: ProbabilityPlot[data1, data2]

Properties & Relations  (8)

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

Wolfram Language code: data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];
Wolfram Language code: {ProbabilityPlot[data], ProbabilityPlot[data, NormalDistribution[μ, σ]]}

QuantilePlot compares quantiles for the data:

Wolfram Language code: data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];
Wolfram Language code: QuantilePlot[data]

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

Wolfram Language code: data = RandomVariate[NormalDistribution[1, 2], 10 ^ 3];
Wolfram Language code: ProbabilityScalePlot[data, "Normal"]

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

Wolfram Language code: data = RandomVariate[ExponentialDistribution[2], 10 ^ 3];
Wolfram Language code: {BoxWhiskerChart[data], DistributionChart[data]}

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

Wolfram Language code: data = RandomVariate[ExponentialDistribution[2], 10 ^ 3];
Wolfram Language code: {SmoothHistogram[data, Automatic, "CDF"], Histogram[data, Automatic, "CDF"]}

DiscretePlot can be used to visualize the discrete distributions:

Wolfram Language code: {ProbabilityPlot[PoissonDistribution[3]], DiscretePlot[CDF[PoissonDistribution[3], x], {x, 0, 6}, PlotStyle -> PointSize[Medium]]}

Use ListPlot to see the data:

Wolfram Language code: data = FindClusters[RandomVariate[ExponentialDistribution[2], 100]];
Wolfram Language code: ListPlot[data]

ProbabilityPlot ignores time stamps when input is a TimeSeries:

Wolfram Language code: data = TemporalData[TimeSeries, {{{-1.2851063764241863, 1.8324042559834568, 4.644950609531538, 1.509265945417493, 1.8128859551454304, 3.1813846692402996, 2.171122557373735, 1.5336042672985486, 1.419469763349254, -0.2663059484359207, 0.3409179135 ... 18797615790018, -1.2241389048830675, 2.059880322321172, -0.36363794430027485, 0.4890752692327103}}, {{0, 999, 1}}, 1, {"Continuous", 1}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: {ProbabilityPlot[data], ProbabilityPlot[data["Values"]]}

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) ▪ 2026 (15.0)

Wolfram Research (2010), ProbabilityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbabilityPlot.html (updated 2026).

Text

Wolfram Research (2010), ProbabilityPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbabilityPlot.html (updated 2026).

CMS

Wolfram Language. 2010. "ProbabilityPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2026. 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_2026_probabilityplot, author="Wolfram Research", title="{ProbabilityPlot}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/ProbabilityPlot.html}", note=[Accessed: 01-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_probabilityplot, organization={Wolfram Research}, title={ProbabilityPlot}, year={2026}, url={https://reference.wolfram.com/language/ref/ProbabilityPlot.html}, note=[Accessed: 01-September-2026]}

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