Difference between revisions of "SDeviation"

 
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[[category:Statistical Functions]]
 
[[category:Statistical Functions]]
 
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[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
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== SDeviation(X, ''I, w'') ==
 
Computes the weighted sample standard deviation -- the square root of the [[Variance|variance]].
 
Computes the weighted sample standard deviation -- the square root of the [[Variance|variance]].
  
= Simple Usage =
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If ''X'' is an uncertain quantity, dependent on Analytica distribution functions, the variance is obtained using  [[SDeviation]](X).
  
If ''X'' is an uncertain quantity, dependent on Analytica distribution functions, the variance is obtained using
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«X» is evaluated in [[Sample]] mode, and the variance along the [[Run]] index computed.
  
SDeviation(X)
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Regardless of the variation used, the standard deviation, or weighted standard deviation, is defined as
  
X is evaluated in sample mode, and the variance along the [[Run]] index computed.
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:<math>\sqrt(Variance(X,I,w))</math>
  
= Standard Deviation along Index =
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See [[Variance]] for additional technical details.
  
Given a data set indexed by I, the sample variance along I is computed using:
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==Optional parameters==
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===I===
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The optional «I» parameter can be used to calculate standard deviation along Index «I».
  
SDeviation(X,I)
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Given a data set indexed by «I», the sample variance along «I» is computed using:
  
When the running index, I, is the system index [[Run]] (or not specified), the value of X is evaluated in Sample mode and the average value among numeric values computed. If the running index is anything other than Run, then X is evaluated in context.
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:<code>SDeviation(X, I)</code>
  
= Weighted SDeviation =
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When the running index, «I», is the system index [[Run]] (or not specified), the value of «X» is evaluated in [[Sample]] mode and the average value among numeric values computed. If the running index is anything other than [[Run]], then «X» is evaluated in context.
  
The weighted standard deviation computing by assigning a different "weight" to each point.  The weight vector, wt, should be indexed by I (or by Run if I is not specified), and the weighted variance is computed using one of these forms
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=== W ===
  
  SDeviation(X,w:wt)
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The weighted standard deviation computing by assigning a different "weight" to each point. The weight vector, <code>wt</code>, should be indexed by «I» (or by [[Run]] if «I» is not specified), and the weighted variance is computed using one of these forms
SDeviation(X,I,w:wt)
 
  
When the w parameter is not specified, and the running index I is either the Run index or is not specified, then the weighting defaults to the value in the system variable [[SampleWeighting]].
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:<code>SDeviation(X, w: wt)</code>
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:<code>SDeviation(X, I, w: wt)</code>
  
= Description =
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When the «w» parameter is not specified, and the running index «I» is either the [[Run]] index or is not specified, then the weighting defaults to the value in the system variable [[SampleWeighting]].
 
 
Regardless of the variation used, the standard deviation, or weighted standard deviation, is defined as
 
$\sqrt(Variance(X,I,w))$
 
 
 
See [[Variance]] for additional technical details.
 
 
 
= See Also =
 
  
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== See Also ==
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* [[Statistical_functions#Sdeviation.28x.29|Statistical functions: SDeviation]]
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* [[Statistical Functions and Importance Weighting]]
 
* [[Variance]]
 
* [[Variance]]
* [[Statistical Functions and Importance Weighting]]
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* [[Mean]]
* [[Mean]], [[Skewness]], [[Kurtosis]].
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* [[Skewness]]
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* [[Kurtosis]]
 
* [[Statistics]]
 
* [[Statistics]]
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* [[media:Data Statistics Library.ana|Data Statistics Library.ana]]
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* [[Analytica_Libraries_and_Templates#Data_Statistics|Data Statistics library]]

Latest revision as of 23:10, 22 August 2016


SDeviation(X, I, w)

Computes the weighted sample standard deviation -- the square root of the variance.

If X is an uncertain quantity, dependent on Analytica distribution functions, the variance is obtained using SDeviation(X).

«X» is evaluated in Sample mode, and the variance along the Run index computed.

Regardless of the variation used, the standard deviation, or weighted standard deviation, is defined as

[math]\displaystyle{ \sqrt(Variance(X,I,w)) }[/math]

See Variance for additional technical details.

Optional parameters

I

The optional «I» parameter can be used to calculate standard deviation along Index «I».

Given a data set indexed by «I», the sample variance along «I» is computed using:

SDeviation(X, I)

When the running index, «I», is the system index Run (or not specified), the value of «X» is evaluated in Sample mode and the average value among numeric values computed. If the running index is anything other than Run, then «X» is evaluated in context.

W

The weighted standard deviation computing by assigning a different "weight" to each point. The weight vector, wt, should be indexed by «I» (or by Run if «I» is not specified), and the weighted variance is computed using one of these forms

SDeviation(X, w: wt)
SDeviation(X, I, w: wt)

When the «w» parameter is not specified, and the running index «I» is either the Run index or is not specified, then the weighting defaults to the value in the system variable SampleWeighting.

See Also

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