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Algorithm for error-free determination of the variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement data

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  • Andrzej Chmielowiec

    (Rzeszow University of Technology)

Abstract

The article presents an algorithm for fast and error-free determination of statistics such as the arithmetic mean and variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement data. Additionally, it shows that both floating-point and integer representation can be used to perform this kind of statistical calculations. The author proves a theorem on the number of bits of precision that an arithmetic type must have to guarantee error-free determination of the arithmetic mean and variance. The article also presents the extension of Welford’s formula for determining variance for the sliding window method—determining the variance of fixed-length contiguous subsequences. The section dedicated to implementation tests shows the running times of individual algorithms depending on the arithmetic type used. The research shows that the use of integers in calculations makes the determination of the aforementioned statistics much faster.

Suggested Citation

  • Andrzej Chmielowiec, 2021. "Algorithm for error-free determination of the variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement data," Computational Statistics, Springer, vol. 36(4), pages 2813-2840, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01096-1
    DOI: 10.1007/s00180-021-01096-1
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    References listed on IDEAS

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    1. Douglas M. Hawkins, 1980. "Critical Values for Identifying Outliers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 95-96, March.
    2. Philippe Pébay & Timothy B. Terriberry & Hemanth Kolla & Janine Bennett, 2016. "Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights," Computational Statistics, Springer, vol. 31(4), pages 1305-1325, December.
    3. Katie Evans & Tanzy Love & Sally Thurston, 2015. "Outlier Identification in Model-Based Cluster Analysis," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 63-84, April.
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