Generalized Mean - Properties

Properties

  • Like most means, the generalized mean is a homogeneous function of its arguments . That is, if b is a positive real number, then the generalized mean with exponent p of the numbers is equal to b times the generalized mean of the numbers .
  • Like the quasi-arithmetic means, the computation of the mean can be split into computations of equal sized sub-blocks.
M_p(x_1,\dots,x_{n\cdot k}) = M_p(M_p(x_1,\dots,x_{k}), M_p(x_{k+1},\dots,x_{2\cdot k}), \dots, M_p(x_{(n-1)\cdot k + 1},\dots,x_{n\cdot k}))

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