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ProbabilityScalePlot

ProbabilityScalePlot [{x1,x2,…}]

generates a normal probability plot of the samples xi.

ProbabilityScalePlot [{x1,x2,…},"dist"]

generates a probability plot scaled for the distribution "dist".

ProbabilityScalePlot [{data1,data2,…},"dist"]

generates several scaled probability plots for data1, data2, ….

Details and Options

Examples

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Basic Examples  (3)

A normal probability plot compared to an estimated normal distribution:

A Weibull probability plot:

Normal probability plot of several datasets with a legend:

Scope  (30)

Data  (13)

ProbabilityScalePlot works with numeric data:

ProbabilityScalePlot with multiple datasets:

Normal probability plot:

A Weibull probability plot:

An exponential probability plot:

Lognormal probability plot:

Rayleigh probability plot:

Fréchet probability plot:

Gumbel probability plot:

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  (16)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Include legends for each dataset:

Use Legended to provide a legend for a specific dataset:

Add labels:

Use specific styles for the reference line:

Turn off the reference line:

Draw grid lines:

Provide an interactive Tooltip for the data:

Create filled plots:

Use shapes to distinguish different datasets:

Use Joined to connect datasets with lines:

Use a theme to create a black-and-white plot:

Reverse the direction of the x axis:

Plots usually have 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  (78)

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  (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  (7)

Fill from 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 bottom:

Fill between datasets using a particular style:

Use different styles above and below the filling level:

Filling only applies where the datasets overlap:

FillingStyle  (2)

Use different fill colors:

Fill with transparent orange regions:

GridLines  (1)

Use automatically computed grid lines:

GridLinesStyle  (1)

Use light gray grid lines:

Joined  (1)

Datasets are not joined by default:

Join the points:

Mesh  (4)

Use 20 mesh levels evenly spaced in the direction:

Use the mesh to divide the curve into deciles:

Use an explicit list of values for the mesh:

Specify mesh positions and styles:

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 the 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:

Method  (3)

By default a reference line is drawn through the first and third quartiles of data:

Draw the best-fit line through data:

The reference line represents the reference distribution:

PlotHighlighting  (9)

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 a set of points to highlight it using arbitrary graphics directives:

Move the mouse over the points to highlight them with balls and labels:

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 plot closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the points 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)

QuantilePlot 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:

Use plot markers:

PlotRange  (3)

PlotRange is automatically calculated:

Show the whole dataset:

Show the distribution for between 1 and 3 and between 90 and 99:

PlotStyle  (3)

Use different style directives:

By default different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotTheme  (1)

Use a theme to create a black-and-white plot:

Use a solid, light gray reference line:

ReferenceLineStyle  (3)

ReferenceLineStyle by default uses a Dotted form of PlotStyle :

Draw a red dotted reference line:

Draw a solid red reference line:

Use None to turn off the reference line:

ScalingFunctions  (2)

By default ProbabilityScalePlot uses an automatic scale on both of the axes:

Reverse the direction of the x axis:

Applications  (2)

A group of ecologists surveyed an island's bird species populations. For each species on the island, the number of individuals observed was recorded. Often LogNormalDistribution is used to model abundance of species:

It appears that a lognormal model is a reasonable choice:

Find the best-fitting LogNormalDistribution using a maximum likelihood estimation:

Normal probability plot for a time slice of a random process:

Properties & Relations  (8)

Compare data with different reference distributions:

Compare the quantiles of data with quantiles of a normal distribution:

Compare the CDF of the data with the CDF of a normal distribution:

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 discrete distributions:

Use ListPlot to see the data:

ProbabilityScalePlot ignores time stamps when input is a TimeSeries :

See Also

QuantilePlot   ProbabilityPlot   EstimatedDistribution   CDF   SmoothKernelDistribution

History

Introduced in 2010 (8.0) | Updated in 2012 (9.0) ▪ 2014 (10.0) ▪ 2022 (13.1) ▪ 2023 (13.3) ▪ 2025 (14.2)

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_probabilityscaleplot, author="Wolfram Research", title="{ProbabilityScalePlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html}", note=[Accessed: 12-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_probabilityscaleplot, organization={Wolfram Research}, title={ProbabilityScalePlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ProbabilityScalePlot.html}, note=[Accessed: 12-April-2025 ]}
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