Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments

摘要

We present a formula for the pairwise update of arbitrary-order centered statistical moments. This formula is of particular interest to compute such moments in parallel for large-scale, distributed data sets. As a corollary, we indicate a specialization of this formula for incremental updates, of particular interest to streaming implementations. Finally, we provide pairwise and incremental update formulas for the covariance.