WOLFRAM

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

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

Examples

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Basic Examples  (4)Summary of the most common use cases

A normal probability plot compared to an estimated normal distribution:

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Compare to the standard normal distribution:

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A probability-probability plot of two datasets:

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Plot several datasets with a legend:

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Scope  (26)Survey of the scope of standard use cases

Data and Distributions  (12)

ProbabilityPlot works with numeric data:

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ProbabilityPlot works with symbolic distributions:

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Use multiple datasets and distributions:

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The default reference distribution is the closest estimated NormalDistribution:

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Specify data or distributions as the reference:

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Reference distributions are estimated for each dataset:

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Estimate specific reference distributions for numeric datasets:

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Use all forms of built-in distributions:

Parametric:

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Nonparametric:

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Derived:

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Plot values with units:

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Plot the values from an association:

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Plot data with weights:

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Plot data from time series:

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Tabular Data  (1)

Get tabular data:

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Compare the data to a normal distribution:

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Compare multiple sets of data:

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

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Compare probability of sepal width per species:

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

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Use legends for the plot:

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Presentation  (13)

Multiple datasets are automatically colored to be distinct:

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Provide explicit styling to different sets:

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Include legends for each dataset:

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Add labels:

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Use specific styles for the reference line:

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Turn off the reference line:

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Provide an interactive Tooltip for the data:

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Provide a specific tooltip for the data:

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Create filled plots:

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Use shapes to distinguish different datasets:

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Use Joined to connect datasets with lines:

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Use a theme with grid lines:

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

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

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Choose from multiple interactive highlighting effects:

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Options  (67)Common values & functionality for each option

ColorFunction  (6)

ColorFunction requires at least one dataset to be Joined:

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Color by scaled and coordinates:

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Color with a named color scheme:

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

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ColorFunction has higher priority than PlotStyle for coloring the curve:

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Use Automatic in MeshShading to use ColorFunction:

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ColorFunctionScaling  (2)

Color the line based on scaled value:

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Color the line based on unscaled value:

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Filling  (6)

Fill from the data to the reference line:

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Use symbolic or explicit values for filling:

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Points fill with stems:

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Curves fill with solid regions:

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Fill from the third dataset to the axis:

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Fill between datasets using a particular style:

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Use different styles above and below the filling level:

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FillingStyle  (2)

Use different fill colors:

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Use a transparent orange filling:

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Joined  (2)

Datasets are not joined by default:

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Join the points:

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Symbolic distributions are joined by default:

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Mesh  (3)

Use 20 mesh levels evenly spaced in the direction:

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Use the mesh to divide the curve into deciles:

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Specify Style and mesh levels in the direction:

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MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

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

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MeshShading  (6)

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

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Use None to remove segments:

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MeshShading can be used with PlotStyle:

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MeshShading has higher priority than PlotStyle for styling the curve:

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Use PlotStyle for some segments by setting MeshShading to Automatic:

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MeshShading can be used with ColorFunction:

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MeshStyle  (4)

Color the mesh the same color as the plot:

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Use a red mesh in the direction:

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

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Use big red mesh points in the direction:

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PlotHighlighting  (8)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

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Use PlotHighlightingNone to disable the highlighting for the entire plot:

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

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

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

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

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

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Specify the style for the points:

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

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Use Callout options to change the appearance of the label:

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Combine components to create a custom effect:

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PlotLegends  (7)

By default, no legends are used:

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Generate a legend using labels:

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Generate a legend using placeholders:

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Legends use the same styles as the plot:

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Use Placed to specify the legend placement:

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Place the legend inside the plot:

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Use LineLegend to change the legend appearance:

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PlotMarkers  (7)

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

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Automatically use colors and shapes to distinguish sets of data:

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Use shapes only:

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Change the size of the default plot markers:

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Use arbitrary text for plot markers:

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Use explicit graphics for plot markers:

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Use the same symbol for all the sets of data:

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PlotStyle  (3)

Use different style directives:

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By default, different styles are chosen for multiple curves:

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Explicitly specify the style for different curves:

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PlotTheme  (2)

Use a theme with grid lines:

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Use a theme with high-contrast colors:

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Turn off the grid lines:

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ReferenceLineStyle  (4)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

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Draw a dotted red reference line:

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Draw a solid red reference line:

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Use None to turn off the reference line:

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ReferenceLineStyle can be combined with PlotStyle:

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ScalingFunctions  (2)

Data is normally shown on linear scales:

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Plot the data on a log-scaled axis:

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Applications  (3)Sample problems that can be solved with this function

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

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

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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:

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

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Compare two time slices for a random process:

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Properties & Relations  (8)Properties of the function, and connections to other functions

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

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QuantilePlot compares quantiles for the data:

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

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

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

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DiscretePlot can be used to visualize the discrete distributions:

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Use ListPlot to see the data:

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ProbabilityPlot ignores time stamps when input is a TimeSeries:

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

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.

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

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: 28-March-2025 ]}

@misc{reference.wolfram_2025_probabilityplot, author="Wolfram Research", title="{ProbabilityPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ProbabilityPlot.html}", note=[Accessed: 28-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_probabilityplot, organization={Wolfram Research}, title={ProbabilityPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ProbabilityPlot.html}, note=[Accessed: 28-March-2025 ]}

@online{reference.wolfram_2025_probabilityplot, organization={Wolfram Research}, title={ProbabilityPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ProbabilityPlot.html}, note=[Accessed: 28-March-2025 ]}