This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# 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 generates a plot of the CDF of data against the CDF of rdata. ProbabilityPlotgenerates a plot of the CDF of data against the CDF of symbolic distribution rdist. ProbabilityPlotgenerates a plot of the CDF of against the CDF of a reference distribution ref.
• ProbabilityPlot works with 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.
• The form or 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
 AspectRatio 1/GoldenRatio ratio of width to height ClippingStyle Automatic what to draw where curves are clipped ColorFunction Automatic how to determine the coloring of curves ColorFunctionScaling True whether to scale arguments to ColorFunction Filling None filling to insert under each curve FillingStyle Automatic style to use for filling Joined Automatic whether to join points Mesh None how many mesh points to draw on each curve MeshFunctions {#1&} how to determine the placement of mesh points MeshShading None how to shade regions between mesh points MeshStyle Automatic the style for mesh points Method Automatic methods to use PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotMarkers None markers to use to indicate each point for datasets PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to specify the style for each object ReferenceLineStyle Automatic style for the reference line ScalingFunctions None how to scale individual coordinates WorkingPrecision MachinePrecision the precision used in internal computations for symbolic distributions
• With Filling, 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 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:
Compare to the standard normal distribution:
A probability-probability plot of two datasets:
Plot several datasets:
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:
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 Scope   (17)
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:
Multiple datasets are automatically colored to be distinct:
Provide explicit styling to different sets:
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:
 Options   (52)
Choose the ratio of height to width from the actual plot values:
Draw axes instead of a frame:
Use labels based on variables specified:
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 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:
Use different fill colors:
Use a transparent orange filling:
Datasets are not joined by default:
Join the points:
Symbolic distributions are joined by default:
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:
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 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:
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:
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:
ReferenceLineStyle can be combined with PlotStyle:
Data is normally shown on linear scales:
Plot the data on a log-scaled axis:
 Applications   (2)
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 t-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:
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 distrete distributions:
Use ListPlot to see the data:
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