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[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)

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 with a legend:

Scope  (23)

Data and Distributions  (12)

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:

Plot values with units:

Plot the values from an association:

Plot data with weights:

Plot data from time series:

Presentation  (11)

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Include legends for each dataset:

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:

Use a theme with grid lines:

Options  (61)

AspectRatio  (1)

Choose the ratio of height to width from the actual plot values:

Axes  (1)

Draw axes instead of a frame:

AxesLabel  (1)

Use labels based on variables specified:

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  (6)

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:

FillingStyle  (2)

Use different fill colors:

Use a transparent orange filling:

Joined  (2)

Datasets are not joined by default:

Join the points:

Symbolic distributions are joined by default:

Mesh  (3)

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:

MeshFunctions  (2)

Use a mesh evenly spaced in the and directions:

Show 5 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 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:

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)

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:

PlotStyle  (3)

Use different style directives:

By default, different styles are chosen for multiple curves:

Explicitly specify the style for different curves:

PlotTheme  (2)

Use a theme with grid lines:

Use a theme with high-contrast colors:

Turn off the grid lines:

ReferenceLineStyle  (4)

ReferenceLineStyle by default uses a Dotted form of PlotStyle:

Draw a dotted red reference line:

Draw a solid red reference line:

Use None to turn off the reference line:

ReferenceLineStyle can be combined with PlotStyle:

ScalingFunctions  (2)

Data is normally shown on linear scales:

Plot the data on a log-scaled axis:

Applications  (3)

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:

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

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:

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

Compare two time slices for a random process:

Properties & Relations  (8)

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 discrete distributions:

Use ListPlot to see the data:

ProbabilityPlot ignores time stamps when input is a TimeSeries:

Introduced in 2010
 (8.0)
 |
Updated in 2012
 (9.0)
2014
 (10.0)