Program/Track B/B.1.3/Welford’s algorithm for accurate computation of weighted mean, variance, and covariance
Welford’s algorithm for accurate computation of weighted mean, variance, and covariance
Alexey Shagraev, Andrey Efanov, Sergey Ivliev
The Wellford method is a simple and effective way to calculate averages, variances, covariances, and other statistics. This method has several excellent properties: • achieves high performance on the accuracy of decisions; • it is straightforward to understand and implement; • it is a one-pass online algorithm, which is extremely useful in some situations. Wellford’s original article published in 1962. Nevertheless, the algorithm is not widely known at present. Moreover, it is a non-trivial task to find a mathematical proof of its correctness or experimental comparisons with other methods. This article attempts to fill these gaps.