The methods of updating central moments are often covered in various works where the large updating samples are present. However, absolute central moments of odd orders still remain unaddressed. In online systems and systems that are highly dependent on data transfer speed the issue of updating the absolute central moment of a time series on a certain constantly updating sample often comes up. In this paper we will propose a method for fast update of absolute central moments of time series and its programmatic implementation based on the treap data structure.

 

absolute central moments, treap, online systems, central moments.

 

Стр. 3-11.

 

DOI 10.14357/20718632210101

 

 

References

1. G. Kramer. Matematicheskie metodi statistiki. — 2-nd publ. — M.: Mir, 1975. — P. 196-197, 284. — 648 p.

2. Gueron S. Efficient software implementations of modular exponentiation //Journal of Cryptographic Engineering. – 2012. – Т. 2. – №. 1. – С. 31-43.

3. Pébay P. et al. Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights //Computational Statistics. – 2016. – Т. 31. – №. 4. – С.1305-1325.

4. K. Bulatov, N. Fedotova, V. V. Arlazarov, Fast Approximate Modelling of the Next Combination Result for Stop-ping the Text Recognition in a Video //In Proc. 2020 25th International Conference on Pattern Recognition (ICPR) Milan, Italy, Jan 10-15, 2021, p. 239-246.

5. V. V. Arlazarov, A. E. Zhukovskiy, V. E. Krivtsov, D. P. Nikolaev and D. V. Polevoy, “Analiz osobennostey ispolzovaniya statsionarnykh i mobilnykh malorazmernykh tsifrovykh video kamer dlya raspoznavaniya dokumentov,” ITiVS, no 3, pp. 71-81, 2014.

6. Bulatov K. B. A Method to Reduce Errors of String Recognition Based on Combination of Several Recognition Results with Per-Character Alternatives // Вестник ЮУрГУ ММП. — 2019. — Т. 12. — № 3. — С. 74-88. — DOI: 10.14529/mmp190307.

7. Bulatov K., Savelyev B., Arlazarov V. V. Next integrated result modelling for stopping the text field recognition process in a video using a result model with per-character alternatives // ICMV 2019 / Wolfgang Osten, Dmitry Nikolaev, Jianhong Zhou. — SPIE. — янв. 2020. — Т. 11433. — ISSN 0277-786X. — ISBN 978-15-10636-44-6. — 2020. — Т. 11433. — 11433 2M. — С. 1-7. — DOI: 10.1117/12.2559447. 

8. Adelson-Velsky, Georgy; Landis, Evgenii (1962). "An algorithm for the organization of information". Proceedings of the USSR Academy of Sciences (in Russian). 146: 263–266.

9. Storer J. A. An introduction to data structures and algorithms. – Springer Science & Business Media, 2012.

10. Blelloch G. E., Reid-Miller M. Fast set operations using treaps //Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures. – 1998. – С. 16-26.

11. Seidel R., Aragon C. R. Randomized search trees //Algorithmica. – 1996. – Т. 16. – №. 4-5. – С. 464-497.