Difference between revisions of "Skewness"

Revision as of 04:15, 20 August 2015

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 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.

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-#REDIRECT [[Statistical Functions and Importance Weighting#Skewness]]
 [[category:Statistical Functions]]
+== Skewness(x'', i, w'') ==
+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>
+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.
+== See also ==
+* [[Statistical Functions and Importance Weighting]]