Minkowski Mean

By Kardi Teknomo, PhD .

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Minkowski Mean

Minkowski mean is a generalization of arithmetic , quadratic and harmonic mean .

Minkowski mean is defined as

Example:

When , we have Arithmetic mean

Example:

When , we have Harmonic mean

Example :

When p=2, we have Quadratic mean

However, we do not have a specific p in Minkowski mean to represent Geometric mean because Geometric mean is obtained through the limit of parameter p approaches 0, indicated by the formula below

Use the interactive program below to compute Harmonic mean of a list of numbers separated by comma. You may change with your own input values. Try to change the parameter p to a small number but not zero such as 0.0000000001 and compare the result with Geometric Mean .

Table below provides the summary of parameter to relate Minkowski generalized mean and other means.