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If we were to ignore numerical accuracy we could use a simple derivation to show that the following updates for is very large.

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(It is not the only alternative, for a detailed numerical study of possible options, see the paper linked below.) The West algorithm supports mean and variance computation for positively weighted samples Alternative algorithms and variants for higher-order moments can be found on the excellent Wikipedia page on the topic.

Addendum: (October 2015) A recent paper by (Meng, 2015) contains a variant of the above algorithm for the unweighted case to compute the first four central moments in a numerically stable manner.

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