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Archimedian 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) suggests Archimedean double mean process as 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 Gaussian Double mean process .
The Archimedean double mean process has a very nice property that the sequence and will converge to a common limit with linear convergence rate. However, the common limit is not necessarily produce means. For example, if we use arithmetic and geometric mean respectively, we will get which is not means or average.
Example: (Archimedean harmonicgeometric mean)
We use harmonic mean and geometric mean
and
Then the sequence and will converge to a common limit
For instance:
, ,
,
Notice that this Archimedean harmonicgeometric mean is not symmetric mean, because in general, .
Note that
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See also:
Gaussian Double Mean Process
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This tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Mean and Average. http:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\