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 =
æ ç
è
Spn
ö ÷
ø
[1/p]
, Sp = x1p+ ... +
xnp
Many well known means are special cases
p
Name
-infinity
Minimum
-1
Harmonic
0
Geometric
1
Arithmetic
2
Quadratic
infinity
Maximum
I have prepared a translation
of his article
on a generalisation
of algebraic means.
Available as PDF version
I am investigating producing an HTML one. E-mail
me for details.
This page was last modified
no earlier than October 2003