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Statistics

 Support
 compute the support set of a random variable

 Calling Sequence Support(X, t, opts) Support(X, opts)

Parameters

 X - algebraic; random variable or distribution t - algebraic; any expression opts - (optional) equation of the form output = form, specifying what form the output should have

Description

 • Given a random variable X with probability density function $f$, the Support function will find a set A of real numbers such that $f\left(x\right)=0$ for all $x$ not in A. This set can be used to estimate the size of the support of X.
 • There are three forms of output that Support can return.
 If called with the $\mathrm{output}=\mathrm{property}$ option, then Support returns a property that points in the set A have, typically of the form RealRange(a, b). Note that only numeric ranges can be represented in this way.
 If called with the $\mathrm{output}=\mathrm{boolean}$ option, then Support returns a boolean expression expressing that t is in A, typically of the form $a\le t\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}t.
 If called with the $\mathrm{output}=\mathrm{range}$ option, then Support returns a range describing A, of the form $a..b$.
 If called without an $\mathrm{output}$ option, then the default is the $\mathrm{property}$ format if t is not given and $\mathrm{boolean}$ format if t is given.
 • The first parameter can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
 • The second parameter can be any algebraic expression. It is a necessary argument for $\mathrm{output}=\mathrm{boolean}$ and ignored otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$

Compute the support of the normal distribution.

 > $\mathrm{Support}\left(\mathrm{Normal}\left(3,1\right)\right)$
 ${\mathrm{real}}$ (1)
 > $\mathrm{Support}\left(\mathrm{Normal}\left(3,1\right),'\mathrm{output}=\mathrm{range}'\right)$
 ${-}{\mathrm{∞}}{..}{\mathrm{∞}}$ (2)
 > $\mathrm{Support}\left(\mathrm{Uniform}\left(3,5\right)\right)$
 ${\mathrm{RealRange}}{}\left({3}{,}{\mathrm{Open}}{}\left({5}\right)\right)$ (3)
 > $\mathrm{Support}\left(\mathrm{Binomial}\left(10,0.5\right)\right)$
 ${\mathrm{RealRange}}{}\left({0}{,}{10}\right)$ (4)
 > $\mathrm{Support}\left(\mathrm{Uniform}\left(3,5\right),t\right)$
 ${3}{\le }{t}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{and}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{t}{<}{5}$ (5)
 > $\mathrm{Support}\left(\mathrm{Uniform}\left(3,5\right),4\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{Support}\left(\mathrm{Uniform}\left(3,5\right),7\right)$
 ${\mathrm{false}}$ (7)

Try another distribution.

 > $T≔\mathrm{Distribution}\left(\mathrm{PDF}=\left(t→\mathrm{piecewise}\left(t<-1,0,t<1,\frac{3{t}^{2}\left(5-t\right)}{10},0\right)\right)\right):$
 > $X≔\mathrm{RandomVariable}\left(T\right):$
 > $\mathrm{Support}\left(X\right)$
 ${\mathrm{RealRange}}{}\left({-}{1}{,}{\mathrm{Open}}{}\left({1}\right)\right)$ (8)
 > $\mathrm{Support}\left(X,t\right)$
 ${-}{1}{\le }{t}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{and}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{t}{<}{1}$ (9)
 > $\mathrm{Support}\left(X,t,'\mathrm{output}=\mathrm{property}'\right)$
 ${\mathrm{RealRange}}{}\left({-}{1}{,}{\mathrm{Open}}{}\left({1}\right)\right)$ (10)
 > $\mathrm{Support}\left(X,t,'\mathrm{output}=\mathrm{boolean}'\right)$
 ${-}{1}{\le }{t}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{and}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{t}{<}{1}$ (11)
 > $\mathrm{Support}\left(X,t,'\mathrm{output}=\mathrm{range}'\right)$
 ${-}{1}{..}{1}$ (12)

References

 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

 • The output option was introduced in Maple 16.
 • For more information on Maple 16 changes, see Updates in Maple 16.

 See Also