QuantilePlot
QuantilePlot[list]
generates a plot of quantiles of list against the quantiles of a normal distribution.
QuantilePlot[dist]
generates a plot of quantiles of the distribution dist against the quantiles of a normal distribution.
QuantilePlot[data,rdata]
generates a plot of the quantiles of data against the quantiles of rdata.
QuantilePlot[data,rdist]
generates a plot of the quantiles of data against the quantiles of a symbolic distribution rdist.
QuantilePlot[{data_{1},data_{2},…},ref]
generates a plot of quantiles of data_{i} against the quantiles of a reference distribution ref.
Details and Options
 QuantilePlot[data_{1},data_{2}] works with data_{i} being either a dataset of real values or a symbolic univariate distribution.
 Data for QuantilePlot can be given in the following forms:

{e_{1},e_{2},…} list of elements with or without wrappers <k_{1}y_{1},k_{2}y_{2},… > association of keys and lengths TimeSeries[…],EventSeries[…],TemporalData[…] time series, event series, and temporal data WeightedData[…],EventData[…] augmented datasets w[{e_{1},e_{2},…},…] wrapper applied to a whole dataset w[{data_{1},data_{1},…},…] wrapper applied to all datasets  For datasets list empirical quantiles are used, and for symbolic distributions dist exact quantiles are used.
 QuantilePlot[data,dist[θ_{1},…]] with symbolic parameters θ_{i} is equivalent to QuantilePlot[data,EstimatedDistribution[data,dist[θ_{1},…]]].
 The form w[data] or w[dist] 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  QuantilePlot 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 PlotLegends None legends for data points 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 PlotTheme $PlotTheme overall theme for the plot 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.
 Typical settings for PlotLegends include:

None no legend Automatic automatically determine legend {lbl_{1},lbl_{2},…} use lbl_{1}, lbl_{2}, … as legend labels Placed[lspec,…] specify placement for legend  With ScalingFunctions>{s_{x},s_{y}}, the coordinate is scaled using s_{x} and the coordinate is scaled using s_{y}.
Examples
open allclose allBasic Examples (5)
Scope (22)
Data and Distributions (11)
QuantilePlot works with numeric data:
QuantilePlot 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 builtin distributions:
Numeric values in an association are used as the coordinates:
Numeric keys and values in an association are used as the and coordinates:
The weights in WeightedData are ignored:
Presentation (11)
Multiple datasets are automatically colored to be distinct:
Provide explicit styling to different sets:
Include legends for each dataset:
Use specific styles for the reference line:
Provide an interactive Tooltip for the data:
Provide a specific tooltip for the data:
Use shapes to distinguish different datasets:
Use Joined to connect datasets with lines:
Options (75)
ClippingStyle (4)
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)
Filling (7)
FillingStyle (3)
Joined (2)
Mesh (4)
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 in the direction:
Specify Style and mesh levels in the direction:
MeshFunctions (2)
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)
Method (4)
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)
QuantilePlot normally uses distinct colors to distinguish different sets of data:
Use colors and shapes to distinguish sets of data:
Change the size of the default plot markers:
Use arbitrary text for plot markers:
PlotRange (3)
PlotRange is automatically calculated:
Show the distribution for between 1 and 2 and between 1 and 3:
PlotStyle (3)
PlotTheme (2)
ReferenceLineStyle (4)
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:
Applications (5)
Visually test whether data was drawn from a particular distribution:
Linearity occurs when the data was drawn from the reference distribution:
Deviations from linearity occur when the data was not drawn from the reference distribution:
The residuals resulting from a LinearModelFit should be normally distributed. Here, some data is simulated with normal and exponential noise of equal variance:
Fit linear models to the simulated data:
There is strong visual evidence that the residuals are not normal in the first model:
DistributionFitTest can be used to make a quantitative statement about normality:
The heights of singers from the New York Choral Society were recorded along with the voice part of each singer. Voice parts, in increasing order of pitch, include bass, tenor, alto, and soprano:
The mean heights for each voice part:
Plotting the height quantiles of Soprano 1 against the other voice parts suggests that there is an additive shift in height with a voice part:
Rainfall, in acrefeet, was recorded from 52 clouds, of which 26 were chosen randomly and seeded with silver oxide:
Clearly, the seeded clouds produce more rain than the control:
A loglog scaled plot suggests that the increase is about one order of magnitude:
Properties & Relations (9)
With no second argument, data is compared against an estimated normal distribution:
Comparing with UniformDistribution[{0,1}] is equivalent to plotting the quantile:
ProbabilityPlot compares CDF values 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:
QuantilePlot ignores time stamps when input is a TimeSeries:
Text
Wolfram Research (2010), QuantilePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantilePlot.html (updated 2014).
CMS
Wolfram Language. 2010. "QuantilePlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/QuantilePlot.html.
APA
Wolfram Language. (2010). QuantilePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuantilePlot.html