compute the covariance/covariance matrix - Maple Help

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Statistics[Covariance] - compute the covariance/covariance matrix

Calling Sequence

Covariance(X, Y, options)

CovarianceMatrix(M, options)

Parameters

M

-

Matrix; data samples

X

-

data set, random variable, or distribution

Y

-

data set, random variable, or distribution

options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the covariance/covariance matrix

Description

• 

The Covariance function computes the covariance of two data sets, or the covariance of two random variables or distributions. The CovarianceMatrix function computes the covariance matrix of multiple data sets.

• 

The first parameter can be a data set (given as e.g. a Vector), a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

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.

Options

  

The 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 Covariance command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Covariance 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.

Examples

withStatistics:

U:=seqi,i=57..77,undefined:

V:=seqsini,i=57..77,undefined:

W:=2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:

CovarianceU,V

HFloatundefined

(1)

CovarianceU,V,ignore

0.226147813941922

(2)

CovarianceU,V,weights=W,ignore=true

0.167449265684222

(3)

M:=MatrixU,V

M:= 22 x 2 MatrixData Type: anythingStorage: rectangularOrder: Fortran_order

(4)

CovarianceMatrixM,ignore

38.50000000000000.2261478139040000.2261478139040000.530662127034365

(5)

See Also

Statistics, Statistics[Computation], Statistics[DescriptiveStatistics]

References

  

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


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