Kurtosis

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

The `KURT` function only accepts one or two vector arguments. If only one vector is entered, the function returns the kurtosis 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 kurtosis, kurt, is a nondimensional quantity which measures the relative peakedness or flatness of a distribution, relative to a normal distribution. A distribution with positive kurtosis is termed leptokurtic; a distribution with negative kurtosis is termed platykurtic. An in-between distribution is termed mesokurtic. The kurtosis is defined by:

where the -3 term makes the value zero for a normal distribution.