  Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for
temporal complexity analysis of real-world phenomena. However, their
relationship with the Hurst exponent as a measure of self-similarity is not
widely studied. Additionally, ApEn and SampEn are susceptible to signal
amplitude changes. A common practice for addressing this issue is to correct
their input signal amplitude by its standard deviation. In this study, we first
show, using simulations, that ApEn and SampEn are related to the Hurst exponent
in their tolerance r and embedding dimension m parameters. We then propose a
modification to ApEn and SampEn called range entropy or RangeEn. We show that
RangeEn is more robust to nonstationary signal changes, and it has a more
linear 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 for
characterisation of epileptic EEG data as a real-world example.
