This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


generates a normal probability plot of the samples .
generates a probability plot scaled for the distribution .
generates several scaled probability plots for , , ....
  • ProbabilityScalePlot uses distribution-specific scales so that if data follows the given distribution, the plot will lie on a straight line.
  • The following distribution-specific scales are supported:
"Normal"normal plot
"Weibull"Weibull plot
"Exponential"exponential plot
"LogNormal"lognormal plot
"Rayleigh"Rayleigh plot
"Frechet"Frechet plot
"Gumbel"Gumbel plot
  • The positions plotted correspond to where are uniform order statistics medians given by Quantile.
  • The data is scaled by distribution-specific transformations and given by:
  • The form provides a wrapper w to be applied to the resulting graphics primitives.
  • 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
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
AspectRatio1/GoldenRatioratio of width to height
ClippingStyleAutomaticwhat to draw where curves are clipped
ColorFunctionAutomatichow to determine the coloring of curves
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
FillingNonefilling to insert under each curve
FillingStyleAutomaticstyle to use for filling
JoinedAutomaticwhether to join points
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
PlotMarkersNonemarkers to use to indicate each point for datasets
PlotRangeAutomaticrange of values to include
PlotRangeClippingTruewhether to clip at the plot range
PlotStyleAutomaticgraphics directives to specify the style for each object
ReferenceLineStyleAutomaticstyle for the reference line
ScalingFunctionsNonehow 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 setting PlotStyle->Automatic uses a sequence of different plot styles for different lines.
  • With ScalingFunctions, the coordinate is scaled using and the coordinate is scaled using .
A normal probability plot compared to an estimated normal distribution:
A Weibull probability plot:
Normal probability plot of several datasets:
A normal probability plot compared to an estimated normal distribution:
Click for copyable input
Click for copyable input
A Weibull probability plot:
Click for copyable input
Click for copyable input
Normal probability plot of several datasets:
Click for copyable input
Click for copyable input
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:
Frechet probability plot:
Gumbel probability plot:
Multiple datasets are automatically colored to be distinct:
Provide explicit styling to different sets:
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:
Draw axes instead of a frame:
Label the axes:
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 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:
Color the line based on scaled value:
Color the line based on unscaled value:
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:
Use different fill colors:
Fill with transparent orange regions:
Use automatically computed grid lines:
Use light gray grid lines:
Datasets are not joined by default:
Join the points:
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:
Use a mesh evenly spaced in the and directions:
Show five mesh levels in the direction (red) and 10 in the direction (blue):
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:
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:
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:
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 is automatically calculated:
Show the whole dataset:
Show the distribution for between 1 and 3 and between 90 and 99:
Use different style directives:
By default different styles are chosen for multiple curves:
Explicitly specify the style for different curves:
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:
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:
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:
New in 8