ProbabilityScalePlot

ProbabilityScalePlot[{x1,x2,}]

generates a normal probability plot of the samples xi.

ProbabilityScalePlot[{x1,x2,},"dist"]

generates a probability plot scaled for the distribution "dist".

ProbabilityScalePlot[{data1,data2,},"dist"]

generates several scaled probability plots for data1, data2, .

Details and Options

  • ProbabilityScalePlot[data,"dist"] uses distribution-specific scales so that if data follows the given distribution, the plot will lie on a straight line.
  • The following distribution-specific scales are supported:
  • "Normal"normal plot
    "Weibull"Weibull plot
    "Exponential"exponential plot
    "LogNormal"lognormal plot
    "Rayleigh"Rayleigh plot
    "Frechet"Fréchet plot
    "Gumbel"Gumbel plot
  • The positions plotted correspond to {xi,yi} where yi are uniform order statistics medians given by Quantile[{x1,x2,},].
  • The data is scaled by distribution-specific transformations and given by:
  • "Exponential"
    "Frechet"
    "Gumbel"
    "LogNormal"
    "Normal"
    "Rayleigh"
    "Weibull"
  • Datasets can be given in the following forms:
  • {x1,x2,}list of samples
    {Quantity[x1,unit],Quantity[x2,unit],}samples with units
    <|k1e1,k2e2,|>association of keys and samples
    WeightedData[],EventData[]augmented datasets
    TimeSeries[],EventSeries[],TemporalData[]time series, event series, and temporal data
    w[{e1,e2,},]wrapper applied to a whole dataset
    w[{data1,data2,}]wrapper applied to all datasets
  • The form w[data] 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
  • ProbabilityScalePlot has the same options as Graphics, with the following additions and changes:
  • AspectRatio1/GoldenRatioratio of width to height
    ClippingStyleAutomaticwhat to draw where curves are clipped
    ColorFunctionAutomatichow to determine the coloring of curves
    ColorFunctionScalingTruewhether to scale arguments to ColorFunction
    FillingNonefilling to insert under each curve
    FillingStyleAutomaticstyle to use for filling
    JoinedAutomaticwhether to join points
    MeshNonehow many mesh points to draw on each curve
    MeshFunctions{#1&}how to determine the placement of mesh points
    MeshShadingNonehow to shade regions between mesh points
    MeshStyleAutomaticthe style for mesh points
    MethodAutomaticmethods to use
    PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
    PlotLegendsNonelegends for data points
    PlotMarkersNonemarkers to use to indicate each point for datasets
    PlotRangeAutomaticrange of values to include
    PlotRangeClippingTruewhether to clip at the plot range
    PlotStyleAutomaticgraphics directives to specify the style for each object
    PlotTheme$PlotThemeoverall theme for the plot
    ReferenceLineStyleAutomaticstyle for the reference line
    WorkingPrecisionMachinePrecisionthe 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 PlotStyle->Automatic uses a sequence of different plot styles for different lines.
  • With the ReferenceLineStyle->None, no reference line will be drawn:
  • Noneno legend
    Automaticautomatically determine legend
    {lbl1,lbl2,}use lbl1, lbl2, as legend labels
    Placed[lspec,]specify placement for legend
  • With ScalingFunctions->{sx,sy}, the coordinate is scaled using sx and the coordinate is scaled using sy.

Examples

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Basic Examples  (3)

A normal probability plot compared to an estimated normal distribution:

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A Weibull probability plot:

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Normal probability plot of several datasets with a legend:

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Scope  (26)

Options  (69)

Applications  (2)

Properties & Relations  (8)

See Also

QuantilePlot  ProbabilityPlot  EstimatedDistribution  CDF  SmoothKernelDistribution

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