<
Previous
|
Next
|
Contents
>
Gaussian Double Mean Process
We can view double mean as a general process to find means of two input numbers
using as a
recurrence
formula of two means.
Philips (2000)
proposed Gaussian double mean process is a difference equation that involves two means
and
with two inputs
and
, which relates to each other using the following formula
Where
Compare this difference equation formula with Archimedean Double mean process .
The Gaussian double mean has a very nice property that the sequence
and
will converge to a common limit
and it converges very fast with quadratic speed.
Example: (Arithmetic Geometric mean)
We use arithmetic and geometric mean, thus the name of this mean is AGM = Arithmetic Geometric mean
and
Philips (2000) shows that the sequence
and
will converge to a common limit
where
For instance:
,
You may notice that AGM is symmetric mean.
Example: ( Harmonic-geometric mean )
We use harmonic mean and geometric mean
and
Compare this with the Archimedean harmonic-geometric mean, the (Gaussian) Harmonic-geometric mean is symmetric.
For instance:
,
<
Previous
|
Next
|
Contents
>
See also:
Archimedean Double mean process
Rate this tutorial or give your comments about this tutorial
This tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Mean and Average. https:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\