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On Entropy of Probability Integral Transformed Time Series.

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This study equalizes time series amplitude distributions using probability integral transformation, revealing its impact on entropy estimation for signal regularity analysis. Findings offer insights into reliable entropy measures for complex data, including cardiovascular signals.

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Biomedical Signal Processing

Background:

  • Entropy estimation is crucial for quantifying time series regularity.
  • Amplitude distribution equalization can alter entropy estimates.
  • Probability integral transformation (PIT) is a method for distribution equalization.

Purpose of the Study:

  • To investigate changes in entropy estimates after applying probability integral transformation to time series.
  • To analyze the impact of amplitude equalization on signal regularity.
  • To derive a reference value for entropy in PIT-transformed signals and evaluate estimation reliability.

Main Methods:

  • Generation and coupling of pseudo-random signals with known distributions (statistical/deterministic methods).
  • Application of moving average filters and non-linear equations for signal dependence.
  • Correlation tests, multifractal spectrum analysis, and probability integral transformation on cardiovascular time series (systolic blood pressure, pulse interval).

Main Results:

  • Changes in entropy estimates were observed after probability integral transformation.
  • A method for deriving a reference entropy value for transformed signals was established.
  • Experimental evaluation confirmed the reliability of entropy estimates concerning matching probabilities.

Conclusions:

  • Probability integral transformation significantly impacts entropy estimates of time series.
  • The derived reference value provides a baseline for entropy in transformed signals.
  • The study validates the reliability of entropy estimation post-transformation, applicable to physiological data analysis.