ProbabilityPlot - Maple Help

Statistics

 ProbabilityPlot
 generate probability plots

 Calling Sequence ProbabilityPlot(A, X, options, plotoptions) ProbabilityPlot['interactive'](A, X)

Parameters

 A - X - distribution or random variable options - (optional) equation(s) of the form option=value where option is one of color, reference, or sorted; specify options for generating the probability plot plotoptions - options to be passed to the plots[display] command

Description

 • The ProbabilityPlot command generates a probability-probability plot of the user-defined theoretical distribution (on the horizontal axis) against the response values (on the vertical axis). The response values are sorted, unless otherwise specified (see sorted option). A random sample of the theoretical distribution, having size equal to the size of data is generated, sorted ascendingly, and plotted against the (ordered) response values.
 • The first parameter, A, specifies the response values that correspond to the y-coordinates of the points in the plot. A copy of the response values is sorted ascendingly in the function (i.e. if sorted is false as it is by default), and is plotted against a sorted random sample of the given theoretical distribution that correspond to the x-coordinates of the plot.
 • The second parameter, X specifies the theoretical distribution.  It can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
 • If the ['interactive'] option is used, then a dialog box appears that allows for customized creation of the plot.

Options

 The options argument can contain one or more of the options shown below. All unrecognized options will be passed to the plots[display] command. See plot/options for details.
 • color=name or list
 This option specifies colors for the points and for the reference line. When a list of colors is given, the set of points and the reference line are colored with the corresponding colors in the list.
 • reference=true or false
 If reference is set to true, the reference line $y=x$ is drawn in the same plot. Default value is true.
 • sorted=true or false
 If sorted is set to true, a sorted (ascending) copy of data is used. Otherwise, if false the original data is used. Default value is false.

Examples

Get a random sample drawn from the normal distribution.

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0,1\right)\right):$
 > $A≔\mathrm{Sample}\left(X,200\right):$

Plot it against the same probability distribution.

 > $\mathrm{ProbabilityPlot}\left(A,\mathrm{Normal}\left(0,1\right)\right)$

Added options can alter the appearance for the plot:

 > $\mathrm{ProbabilityPlot}\left(A,\mathrm{Normal}\left(0,1\right),\mathrm{symbolsize}=20,\mathrm{symbol}=\mathrm{circle},\mathrm{color}=\left["Black","Red"\right],\mathrm{gridlines}\right)$

The command uses MaximumLikelihoodEstimate to compute any unspecified parameters in X.

 > $Y≔\mathrm{RandomVariable}\left(\mathrm{Uniform}\left(a,3\right)\right):$
 > $\mathrm{ProbabilityPlot}\left(A,Y\right)$
 > $\mathrm{ProbabilityPlot}\left(A,\mathrm{Normal}\left(\mathrm{\mu },\mathrm{\sigma }\right)\right)$

Plot it against a different distribution.  This is the command to create the plot from the Plotting Guide.

 > $\mathrm{ProbabilityPlot}\left(A,\mathrm{StudentT}\left(3\right),\mathrm{style}=\mathrm{line}\right)$
 >