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Approximate entropy (ApEn) and sample entropy (SampEn) are widely used fortemporal complexity analysis of real-world phenomena. However, theirrelationship with the Hurst exponent as a measure of self-similarity is notwidely studied. Additionally, ApEn and SampEn are susceptible to signalamplitude changes. A common practice for addressing this issue is to correcttheir input signal amplitude by its standard deviation. In this study, we firstshow, using simulations, that ApEn and SampEn are related to the Hurst exponentin their tolerance r and embedding dimension m parameters. We then propose amodification to ApEn and SampEn called range entropy or RangeEn. We show thatRangeEn is more robust to nonstationary signal changes, and it has a morelinear relationship with the Hurst exponent, compared to ApEn and SampEn.RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1(minimum entropy) and it has no need for signal amplitude correction. Finally,we demonstrate the clinical usefulness of signal entropy measures forcharacterisation of epileptic EEG data as a real-world example.

Range entropy: A bridge between signal complexity and self-similarity