gmean

Generalized mean.

A generalized mean, also known as power mean, Holder mean or Kolmogorov-Negumo function of the mean, is an abstraction of the Pythagorean means included harmonic, geometric, and arithmetic mean.

It is defined as,

Mk = [1/n(x1^k + x2^k + ... + xn^k)]^1/k

where: k is indicator power for the desired mean (-1 = harmonic mean; 0 = geometric mean; 1 = arithmetic mean;2 = root mean square).

Although it is not possible to put k = 0 directly but, according to the L’Hopital’s theorem, the limit as k tends to zero exists,

Mk = lim k->0 [1/n(x1^k + x2^k + ... + xn^k)]^1/k = (x1x2 ... xn)^1/k

Input:
x - Input data vector
k - desired power (-1 = harmonic mean ;0 = geometric mean;1 = arithmetic mean;2 = root mean square)

Output:
y - Desired mean