By Kardi Teknomo, PhD .

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Archimedian Double Mean Process

We can view double mean as a general process to find means of two input numbers Archimedian Double Mean Process using as a recurrence formula of two means.

Philips (2000) suggests Archimedean double mean process as a difference equation that involves two means Archimedian Double Mean Process and Archimedian Double Mean Process with two inputs Archimedian Double Mean Process and Archimedian Double Mean Process , which relates to each other using the following formula

Archimedian Double Mean Process

Where Archimedian Double Mean Process

Compare this difference equation formula with Gaussian Double mean process .

The Archimedean double mean process has a very nice property that the sequence Archimedian Double Mean Process and Archimedian Double Mean Process will converge to a common limit Archimedian Double Mean Process 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 Archimedian Double Mean Process which is not means or average.

Example: (Archimedean harmonic-geometric mean)

We use harmonic mean and geometric mean

Archimedian Double Mean Process and Archimedian Double Mean Process

Then the sequence Archimedian Double Mean Process and Archimedian Double Mean Process will converge to a common limit Archimedian Double Mean Process

Archimedian Double Mean Process

For instance:

Archimedian Double Mean Process , Archimedian Double Mean Process ,

Archimedian Double Mean Process , Archimedian Double Mean Process

Notice that this Archimedean harmonic-geometric mean is not symmetric mean, because in general, Archimedian Double Mean Process .

Note that Archimedian Double Mean Process

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See also: Gaussian Double Mean Process
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Teknomo, Kardi (2015) Mean and Average. http:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\