Validation

Entropy numbers are only useful if you can trust them. Every measure in entroscope is checked against an independent implementation or a closed-form result, and those checks run in CI on every push.

What each measure is checked against

Measure	Reference	Agreement
sample	antropy sample_entropy, EntropyHub SampEn	exact (relative error < 1e-10)
approximate	antropy app_entropy, EntropyHub ApEn	exact
permutation (+ normalized)	antropy perm_entropy, EntropyHub PermEn	exact
spectral (+ normalized)	antropy spectral_entropy(method="fft")	exact
multiscale	EntropyHub MSEn (coarse-graining, fixed tolerance)	exact
shannon	scipy.stats.entropy on the same histogram	exact
differential (dist="normal")	scipy.stats.norm(...).entropy()	exact
transfer	bivariate-Gaussian closed form; Kraskov (2004) analytic mutual information	within 0.05 bits / 0.03 nats

The comparisons run on four signal types (white noise, sine plus noise, an AR(1) process and the chaotic logistic map) so agreement isn't an accident of one input.

Spectral entropy and EntropyHub

EntropyHub's SpecEn uses a different spectral estimator, so its numbers differ from both entroscope and antropy by design. entroscope follows antropy's periodogram-based definition.

Two definitions that were corrected

Cross-checking found two places where entroscope drifted from the published definitions. Both are fixed; results from earlier versions will differ slightly.

• Sample entropy now counts length-m and length-m+1 template matches over the same N - m starting points (Richman & Moorman, 2000). Earlier versions used N - m + 1 templates for the length-m count, which shifted values by about 0.001 to 0.003.
• Multiscale entropy now fixes the tolerance at r * std of the original series and reuses it at every scale (Costa et al., 2002). Earlier versions recomputed it per scale, which made white noise look more complex at coarser scales, the opposite of the textbook result.

Run the checks yourself

pip install -e ".[dev,reference]"
pytest tests/test_reference.py -v

Without the reference extra, the live comparisons are skipped, but the pinned values (recorded from antropy 0.2.2 and EntropyHub 2.0) still run in every test job.