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Statistics

 NormalPlot
 generate normal plots

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

Parameters

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

Description

 • The NormalPlot command produces a probability-probability plot of the normal distribution (on the horizontal axis) against the response values (on the vertical axis). The response values will be sorted, unless otherwise specified (see sorted option). A random sample of the theoretical distribution, having size equal to the size of data will be generated, sorted ascendingly, and plotted against the (ordered) response values.
 • The first parameter, X, are the response values that correspond to the y-coordinates of the points in the plot. A copy of the response values is sorted in ascending order in the function (that is, 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.
 • 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 will be colored with the corresponding colors in the list.
 • mu=deduce or realcons
 The mean of the normal distribution. If mu is set to deduce, the mean will be estimated as the mean of the data sample X.
 • reference=truefalse
 If reference is set to true, the reference line $y=x$ will be drawn in the same plot. The default value is true.
 • sigma=deduce or realcons
 The standard deviation of the normal distribution.  If sigma is set to deduce, the standard deviation will be estimated as the standard deviation of the data sample X.
 • sorted=truefalse
 If sorted is set to true, a sorted (ascending) copy of data is used. Otherwise, if false the original data is used. The default value is false.

Examples

Get a random sample of a normal distribution

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{Statistics}}≔1:$
 > $X≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(5,3\right)\right):$
 > $A≔\mathrm{Sample}\left(X,200\right):$

Estimate the parameters.

 > $\mathrm{NormalPlot}\left(A\right)$
 Deduced value mu = 5.07693254898398 Deduced value sigma = 2.9327818741541

Use the original parameters.

 > $\mathrm{NormalPlot}\left(A,\mathrm{μ}=5,\mathrm{σ}=3\right)$

Plot it against a different distribution.

 > $\mathrm{NormalPlot}\left(A,\mathrm{μ}=4,\mathrm{σ}=4,\mathrm{style}=\mathrm{line},\mathrm{legend}=\left["data","reference"\right]\right)$
 >