Covariance - 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

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $U≔⟨\mathrm{seq}\left(i,i=57..77\right),\mathrm{undefined}⟩:$
 > $V≔⟨\mathrm{seq}\left(\mathrm{sin}\left(i\right),i=57..77\right),\mathrm{undefined}⟩:$
 > $W≔⟨2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5⟩:$
 > $\mathrm{Covariance}\left(U,V\right)$
 ${Float}{}\left({\mathrm{undefined}}\right)$ (1)
 > $\mathrm{Covariance}\left(U,V,\mathrm{ignore}\right)$
 ${-0.226147813941922}$ (2)
 > $\mathrm{Covariance}\left(U,V,\mathrm{weights}=W,\mathrm{ignore}=\mathrm{true}\right)$
 ${-0.167449265684222}$ (3)
 > $M≔\mathrm{Matrix}\left(\left[U,V\right]\right)$
 > $\mathrm{CovarianceMatrix}\left(M,\mathrm{ignore}\right)$
 $\left[\begin{array}{cc}{38.5000000000000}& {-0.226147813941922}\\ {-0.226147813941922}& {0.530662127023855}\end{array}\right]$ (4)

References

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