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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: ( Harmonicgeometric mean )
We use harmonic mean and geometric mean
and
Compare this with the Archimedean harmonicgeometric mean, the (Gaussian) Harmonicgeometric mean is symmetric.
For instance:
,
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See also:
Archimedean Double mean process
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Preferable reference for this tutorial is
Teknomo, Kardi (2015) Mean and Average. https:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\