Difference between revisions of "Skewness"

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.

@@ Line 5: / Line 5: @@
 Computes an estimate of the weighted skewness of a distribution, as given by
- <math>\sum_i w_i \left({x-\bar{x}}\over\sigma\right)^3 / \sum_i w_i</math>
+:<math>\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 skew=NAN.  If min(x)=-INF and max(x)=INF then SKEW=NAN.  If min(x)>-INF and max(x)=INF, then skew is +INF, and if min(x)=-INF, max(x)<INF, skew is -INF.
+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]] is[[NaN]].
+: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 ==
 * [[Statistical Functions and Importance Weighting]]