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Statistics

  

ExpectedValue

  

compute expected values

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

ExpectedValue(A, f, ds_options)

ExpectedValue(M, f, ds_options)

ExpectedValue(X, f, rv_options)

ExpectedValue(X, rv_options)

Parameters

A

-

data sample

M

-

Matrix data set

X

-

algebraic; distribution, random variable

f

-

operator; any function

ds_options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the expected value of a data set

rv_options

-

(optional) equation of the form numeric=value; specifies options for computing the expected value of a random variable

Description

• 

For a data set A (given as e.g. a Vector) or a Matrix data set M, the ExpectedValue function computes the expected value of f with respect to the sample distribution of A or of the columns of M, respectively.

• 

For a random variable X the ExpectedValue command computes the expected value of f(X). If X is an expression involving random variables, then the expected value of X is computed.

• 

The first parameter X is a random variable or an algebraic expression involving random variables.

• 

The second parameter is a function.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

All computations involving data are performed in floating-point; therefore, all data provided must have type[realcons] and all returned solutions are floating-point, even if the problem is specified with exact values.

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

Data Set Options

  

The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.

• 

ignore=truefalse -- This option controls how missing data is handled by the ExpectedValue command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the ExpectedValue command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

• 

weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight 1.

Random Variable Options

  

The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the expected value is computed using exact arithmetic. To compute the expected value numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

XRandomVariableNormala,b:

YRandomVariableNormalc,d:

ExpectedValueX2

a2+b2

(1)

ExpectedValueX+Y

a+c

(2)

ExpectedValueXa2

b2

(3)

ZRandomVariableExponential2:

ASampleZ,105:

ExpectedValueZ2

8

(4)

ExpectedValueA,t→t2

8.00071728582744

(5)

Consider the following Matrix data set.

MMatrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M:=31130114694415271273683907884642878964844995128007

(6)

We compute the expected value of the natural logarithm of each of the column data sets.

ExpectedValueM,ln

1.132592096027196.9703129995667711.6064364945012

(7)

References

  

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

Compatibility

• 

The M parameter was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

Statistics

Statistics[CentralMoment]

Statistics[Computation]

Statistics[Distributions]

Statistics[RandomVariable]

 


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