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Statistics

  

Support

  

compute the support set of a random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

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 fx=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 output=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 output&equals;boolean option, then Support returns a boolean expression expressing that t is in A, typically of the form atandt<b.

  

If called with the output&equals;range option, then Support returns a range describing A, of the form a..b.

  

If called without an output option, then the default is the property format if t is not given and 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 output&equals;boolean and ignored otherwise.

Examples

withStatistics&colon;

Compute the support of the normal distribution.

SupportNormal3&comma;1

real

(1)

SupportNormal3&comma;1&comma;&apos;output&equals;range&apos;

&infin;..&infin;

(2)

SupportUniform3&comma;5

RealRange3&comma;Open5

(3)

SupportBinomial10&comma;0.5

RealRange0&comma;10

(4)

SupportUniform3&comma;5&comma;t

3tandt<5

(5)

SupportUniform3&comma;5&comma;4

true

(6)

SupportUniform3&comma;5&comma;7

false

(7)

Try another distribution.

TDistributionPDF&equals;t&rarr;piecewiset<1&comma;0&comma;t<1&comma;3t25t10&comma;0&colon;

XRandomVariableT&colon;

SupportX

RealRange1&comma;Open1

(8)

SupportX&comma;t

1tandt<1

(9)

SupportX&comma;t&comma;&apos;output&equals;property&apos;

RealRange1&comma;Open1

(10)

SupportX&comma;t&comma;&apos;output&equals;boolean&apos;

1tandt<1

(11)

SupportX&comma;t&comma;&apos;output&equals;range&apos;

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

Statistics

Statistics[Computation]

Statistics[Distributions]

Statistics[RandomVariables]

Statistics[Range]

 


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