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Function List:

C++ API

: kurtosis (x)
: kurtosis (x, flag)
: kurtosis (x, flag, dim)

Compute the sample kurtosis of the elements of x.

The sample kurtosis is defined as 

     mean ((x - mean (x)).^4)
k1 = ------------------------
            std (x).^4

The optional argument flag controls which normalization is used. If flag is equal to 1 (default value, used when flag is omitted or empty), return the sample kurtosis as defined above. If flag is equal to 0, return the "bias-corrected" kurtosis coefficient instead: 

              N - 1
k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1))
         (N - 2)(N - 3)

The bias-corrected kurtosis coefficient is obtained by replacing the sample second and fourth central moments by their unbiased versions. It is an unbiased estimate of the population kurtosis for normal populations.

If x is a matrix, or more generally a multi-dimensional array, return the kurtosis along the first non-singleton dimension. If the optional dim argument is given, operate along this dimension.

See also: var, skewness, moment.

Package: octave