Formulas for robust, parallel computation of arbitraryorder, arbitraryvariate, statistical moments with arbitrary weights and compounding.
Abstract
Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and recall the first generalizations which we had obtained in [P$$\acute0$$8]. We then improve these arbitraryorder, numerically stable onepass formulas to arbitraryvariate formulas which we further extend to arbitrary weights and compound variants. We also develop a generalized correction factor for standard twopass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extendedprecision arithmetic.
 Authors:

 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 The Xiph.Org Foundation, Arlington, VA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLCA), Livermore, CA (United States); The Xiph.Org Foundation, Arlington, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1504207
 Report Number(s):
 SAND20150891
562631
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, and Bennett, Janine Camille. Formulas for robust, parallel computation of arbitraryorder, arbitraryvariate, statistical moments with arbitrary weights and compounding.. United States: N. p., 2015.
Web. doi:10.2172/1504207.
Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, & Bennett, Janine Camille. Formulas for robust, parallel computation of arbitraryorder, arbitraryvariate, statistical moments with arbitrary weights and compounding.. United States. doi:10.2172/1504207.
Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, and Bennett, Janine Camille. Sun .
"Formulas for robust, parallel computation of arbitraryorder, arbitraryvariate, statistical moments with arbitrary weights and compounding.". United States. doi:10.2172/1504207. https://www.osti.gov/servlets/purl/1504207.
@article{osti_1504207,
title = {Formulas for robust, parallel computation of arbitraryorder, arbitraryvariate, statistical moments with arbitrary weights and compounding.},
author = {Pebay, Philippe Pierre and Terriberry, Timothy and Kolla, Hemanth and Bennett, Janine Camille},
abstractNote = {Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and recall the first generalizations which we had obtained in [P$\acute0$8]. We then improve these arbitraryorder, numerically stable onepass formulas to arbitraryvariate formulas which we further extend to arbitrary weights and compound variants. We also develop a generalized correction factor for standard twopass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extendedprecision arithmetic.},
doi = {10.2172/1504207},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2015},
month = {2}
}