Algebraic means

Algebraic means (Italian - medie di potenze) were an interest of Bonferroni's. He wrote extensively on them in his textbook and also published a short article on a generalisation of them. The usual algebraic mean of order or degree p of x1 ... xn (positive), defined as


Mp =

Sp
n


[1/p]

 
,    Sp = x1p+ ... + xnp
Many well known means are special cases
pName
-infinity Minimum
-1Harmonic
0Geometric
1Arithmetic
2Quadratic
infinityMaximum
I have prepared a translation of his article on a generalisation of algebraic means.

This page was last modified no earlier than October 2003