Difference between revisions of "Skewness"

 
 
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#REDIRECT [[Statistical Functions and Importance Weighting]]
 
 
[[category:Statistical Functions]]
 
[[category:Statistical Functions]]
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== Skewness(x'', i, w'') ==
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Computes an estimate of the weighted skewness of a distribution, as given by
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:<math>\sum_i w_i \left({x-\bar{x}}\over\sigma\right)^3 / \sum_i w_i</math>
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A symmetric distribution as zero skew.  A distribution with a heavy right tail (like [[Gamma]], [[LogNormal]]) is positively skewed. A distribution with a heavy left tail has a negative skew.
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If one or more infinite values occur in «x», the [[Skewness]] will be +[[INF]], -[[INF]] or [[NaN]]:
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:If [[Min]](x) = [[INF]] or [[Max]](x) = -[[INF]], then [[Skewness]] is[[NaN]]. 
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:If [[Min]](x) = -[[INF]] and [[Max]](x) = [[INF]] then [[Skewness]] is [[NaN]]. 
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:If [[Min]](x) > -[[INF]] and [[Max]](x) = [[INF]], then [[Skewness]] is +[[INF]].
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:If [[Min]](x) = -[[INF]] and [[Max]](x) < [[INF]], then [[Skewness]] is -[[INF]].
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== See also ==
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* [[Statistical Functions and Importance Weighting]]

Latest revision as of 01:08, 14 January 2016


Skewness(x, i, w)

Computes an estimate of the weighted skewness of a distribution, as given by

[math]\displaystyle{ \sum_i w_i \left({x-\bar{x}}\over\sigma\right)^3 / \sum_i w_i }[/math]

A symmetric distribution as zero skew. A distribution with a heavy right tail (like Gamma, LogNormal) is positively skewed. A distribution with a heavy left tail has a negative skew.

If one or more infinite values occur in «x», the Skewness will be +INF, -INF or NaN:

If Min(x) = INF or Max(x) = -INF, then Skewness isNaN.
If Min(x) = -INF and Max(x) = INF then Skewness is NaN.
If Min(x) > -INF and Max(x) = INF, then Skewness is +INF.
If Min(x) = -INF and Max(x) < INF, then Skewness is -INF.

See also

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