BUILT-IN MATHEMATICA SYMBOL

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.

ProbabilityPlot

generates a plot of the CDF of data against the CDF of symbolic distribution rdist.

ProbabilityPlot

generates a plot of the CDF of

against the CDF of a reference distribution ref.

MORE INFORMATION

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.

ProbabilityPlot with symbolic parameters is equivalent to ProbabilityPlot[data, EstimatedDistribution[data, dist[₁, ...]]].

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

ProbabilityPlot has the same options as Graphics, with the following additions and changes:

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->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.

The setting PlotStyle->Automatic uses a sequence of different plot styles for different lines.

With the ReferenceLineStyle->None, no reference line will be drawn.

With ScalingFunctions, the coordinate is scaled using and the coordinate is scaled using .

EXAMPLES

CLOSE ALL

Basic Examples (4)

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:

Add labels:

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:

Use Automatic in MeshShading to use ColorFunction:

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:

Properties & Relations (7)

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: