plots a CDF of columns in the data against each other.

Details and Options

  • PairwiseProbabilityPlot is also known as a P-P plot matrix.
  • It plots high-dimensional data by creating a grid of individual plots of just two data columns at a time.
  • The plot compares column yi={y1i,y2i,,ymi} against column yj={y1j,y2j,,ymj} by plotting a a probability-probability plot of yi against reference data yj in panel {i,j}.
  • The plot in panel consists of points whose coordinates are , where is the probability that a value in yi is less than the k^(th)-smallest value in yj, for k=TemplateBox[{{{p, _, j},  , n}}, Ceiling].
  • Probability plots can help identify the shapes of the distributions of the data column yi relative to column yj:
  • yi and yj are similarly distributed
    the probability that values are less than x is higher for yi than yj
    the probability that values are less than x is lower for yi than yj
    the probability that values are less than x is higher for yi than yj for smaller values of x
    the probability that values are less than x is higher for yi than yj for larger values of x
  • PairwiseProbabilityPlot takes the same options as ProbabilityPlot, with the following changes and additions:
  • AspectRatio 1ratio of height to width for each panel
    Background Nonebackground to use for each plot
    Frame Automaticwhether to draw frames around each panel
    FrameTicksAutomaticwhether to label frame edges with ticks and labels
    GridLines Automaticwhether to include gridlines in panels
    GridLinesStyleAutomaticstyle for gridlines
    HeaderAlignmentCenterhorizontal and vertical alignments of headers
    HeaderBackground Automaticbackground colors to use for headers
    HeaderDisplayFunctionAutomaticfunction to use to format headers
    Headers Automaticlabels to use for each data column yi
    HeaderStyleNonestyles to use for headers
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotHighlightingAutomatichighlighting effect for points
    PlotLayout Automatichow to arrange the panels
    PlotLegendsAutomaticlegends for data
    PlotMarkersNonemarkers to use to indicate each point
    PlotStyle Automaticgraphics directives to determine styles of points
    PlotTheme $PlotThemeoverall theme for the plot
    Spacings Automatichorizontal and vertical spacings
  • PlotLayout can have the following settings:
  • "Descending"data columns going down and to the right
    "Ascending"data columns going up and to the right
    "DescendingHalfMatrix"lower half of the descending layout
    "AscendingHalfMatrix"upper half of the ascending layout
  • Headers specifies the labels to use for each column in the data, and will generally be displayed above each column and after each row in the final plot.
  • Possible settings include:
  • Noneleave the plot columns and rows unlabeled
    Automaticautomatically label columns and rows
    Allalways include column and row labels
    "Indexed"number the columns and rows 1, 2, , n
    {lbl1,lbl2,,lbln}use the given labels lbli
  • HeaderAlignment determines how data column labels are aligned with regard to the plot columns and rows.
  • HeaderAlignment can take the following forms:
  • Centercenter the labels in the header positions
    {h,v}separate horizontal and vertical alignments within the header position
    {cols,rows}use col for plot columns and row for plot rows
  • HeaderBackground and HeaderStyle can take the following forms:
  • Noneuse ambient styling
    styuse the style sty for all headers
    {sty1, sty2,,styn}use the given styles styifor successive headers
    {cols,rows}use col for plot columns and row for plot rows
  • HeaderDisplayFunction determines how headers are displayed.
  • Possible settings are:
  • Automaticautomatic formatting
    Noneuse unprocessed labels
  • The arguments to ColorFunction are yi1,yi2,,yin. By default, the color function arguments are scaled per data column to be between 0 and 1.
  • Use ColorFunctionScalingNone to use unscaled values, or ColorFunctionScaling{cfsc1,cfsc2,} to selectively scale column values.
  • Possible settings for PlotHighlighting include:
  • Automaticautomatically highlight positions in the panels
    Nonedisable interactive highlighting


open allclose all

Basic Examples  (3)

Create an array of probability plots from data with labeled columns:

Compare all columns in a dataset:

Provide header names for the data:

Options  (29)

AspectRatio  (2)

By default, PairwiseProbabilityPlot uses an equal height-to-width ratio:

Use a fixed height-to-width ratio:

Axes  (3)

By default, Frame is used instead of Axes:

Use AxesTrue to turn on axes:

Turn each axis on independently for all subplots:

Background  (2)

By default, PairwiseProbabilityPlot has a white background:

Set a background color:

Frame  (2)

On PairwiseProbabilityPlot, a frame is drawn on each subplot by default:

Draw a frame on the left and bottom edges of the panels:

GridLines  (2)

By default, PairwiseProbabilityPlot does not draw gridlines:

Draw a background grid:

Headers  (3)

By default, PairwiseProbabilityPlot does not label headers:

Number the columns for unlabeled data:

Provide header names for the columns:

HeaderBackground  (2)

By default, PairwiseProbabilityPlot uses a white header background:

Set a header background color:

ImageSize  (6)

Use named sizes such as Tiny, Small, Medium, and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

PlotLayout  (3)

Switch the orientation of the diagonal elements:

Show plots below the diagonal:

Only show plots above the diagonal:

PlotStyle  (1)

Style the data using PlotStyle:

PlotTheme  (2)

Use a theme to customize the plot:

Change the color scheme:

Spacings  (1)

Change the space between the plots:

Wolfram Research (2023), PairwiseProbabilityPlot, Wolfram Language function,


Wolfram Research (2023), PairwiseProbabilityPlot, Wolfram Language function,


Wolfram Language. 2023. "PairwiseProbabilityPlot." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2023). PairwiseProbabilityPlot. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_pairwiseprobabilityplot, author="Wolfram Research", title="{PairwiseProbabilityPlot}", year="2023", howpublished="\url{}", note=[Accessed: 29-May-2024 ]}


@online{reference.wolfram_2024_pairwiseprobabilityplot, organization={Wolfram Research}, title={PairwiseProbabilityPlot}, year={2023}, url={}, note=[Accessed: 29-May-2024 ]}