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
x - Input data vector
k - desired power (-1 = harmonic mean ;0 = geometric mean;1 = arithmetic mean;2 = root mean square)
y - Desired mean
Antonio Trujillo-Ortiz (2021). gmean (https://www.mathworks.com/matlabcentral/fileexchange/19469-gmean), MATLAB Central File Exchange. Retrieved .
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