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Gaussian Double Mean Process
We can view double mean as a general process to find means of two input numbers
Philips (2000) proposed Gaussian double mean process is a difference equation that involves two means
Where Compare this difference equation formula with Archimedean Double mean process. The Gaussian double mean has a very nice property that the sequence
Example: (Arithmetic Geometric mean) We use arithmetic and geometric mean, thus the name of this mean is AGM = Arithmetic Geometric mean
Philips (2000) shows that the sequence
For instance:
You may notice that AGM is symmetric mean.
Example: ( Harmonic-geometric mean ) We use harmonic mean and geometric mean
Compare this with the Archimedean harmonic-geometric mean, the (Gaussian) Harmonic-geometric mean is symmetric. For instance:
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Preferable reference for this tutorial is Teknomo, Kardi. Mean and Average. http:\\people.revoledu.com\kardi\ tutorial\BasicMath\Average\
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