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Related Experiment Videos

Randomness and degrees of irregularity.

S Pincus, B H Singer

    Proceedings of the National Academy of Sciences of the United States of America
    |March 5, 1996
    PubMed
    Summary

    This study introduces approximate entropy (ApEn) to quantify sequence regularity and randomness, even with short data. ApEn offers a computable measure for assessing randomness in various applications.

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    Area of Science:

    • Computational Statistics
    • Information Theory
    • Probability Theory

    Background:

    • Assessing randomness in sequential data is crucial across many fields.
    • Short data lengths and the need to quantify closeness to randomness pose significant challenges.
    • Existing methods often lack computational efficiency or applicability to short sequences.

    Purpose of the Study:

    • To develop a computable framework for quantifying sequence regularity and randomness.
    • To introduce approximate entropy (ApEn) as a measure of maximal randomness applicable to short sequences.
    • To refine foundational concepts of randomness in probability and number theory using computable rates of convergence.

    Main Methods:

    • Development of approximate entropy (ApEn) for quantifying sequence regularity.
    • Formulation of randomness for infinite sequences, retaining computable features.
    • Utilizing ApEn to determine rates of convergence (deficit from maximal randomness).

    Main Results:

    • ApEn quantifies maximal randomness for sequences of any length, including very short ones (N=5).
    • An infinite sequence formulation of randomness is presented with computable properties.
    • ApEn refines concepts of independence and normality by providing rates of convergence.

    Conclusions:

    • Approximate entropy (ApEn) provides a computationally efficient and versatile method for assessing sequence randomness.
    • ApEn is applicable to diverse fields, including random number generation, shuffling analysis, and bootstrap replicate quality assessment.
    • The framework enhances the understanding of randomness by providing computable measures of deviation from maximal randomness.

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