Skewness

Syntax: | `s = SKEW(x)` `s = SKEW(w,x)`

The `SKEW` function only accepts one or two vector arguments. If only one vector is entered, the function returns the skewness of that vector's data. If two vectors are entered, the first vector holds the weights and the second vector holds the data. The result is always a scalar value.

Suppose that x is a vector with N elements.

A weight vector, w, may be entered as the first argument. The length of w is assumed to also be N. If no weights are entered, let default to `1`, for . Define the total weight:

The mean value, , is defined by

The skewness, or third moment, skew, is a nondimensional quantity that characterizes the degree of asymmetry of a distribution around its mean. The skewness is a pure number that characterizes only the shape of the distribution, and is defined by

A positive value of skewness signifies a distribution with an asymmetric tail extending out towards more positive x; a negative value signifies a distribution whose tail extends out towards more negative x.