Dispersion entropy

dispersion_entropy(x, s = GaussianSymbolization(n_categories = 5);
    m = 3, τ = 1, q = 1, base = MathConstants.e)

Compute the (order-q generalized) dispersion entropy to the given base of the univariate time series x. Relative frequencies of dispersion patterns are computed using the symbolization scheme s with embedding dimension m and embedding delay τ.

Recommended parameter values[Li2018] are m ∈ [2, 3], τ = 1, and n_categories ∈ [3, 4, …, 8] for the Gaussian mapping (defaults to 5).


Dispersion entropy characterizes the complexity and irregularity of a time series. This implementation follows the description in Li et al. (2018)[Li2018], which is based on Azami & Escudero (2018)[Azami2018], additionally allowing the computation of generalized dispersion entropy of order q (default is q = 1, which is the Shannon entropy).

Data requirements

Li et al. (2018) recommends that x has at least 1000 data points.

  • Li2018Li, G., Guan, Q., & Yang, H. (2018). Noise reduction method of underwater acoustic signals based on CEEMDAN, effort-to-compress complexity, refined composite multiscale dispersion entropy and wavelet threshold denoising. Entropy, 21(1), 11.
  • Azami2018Azami, H., & Escudero, J. (2018). Coarse-graining approaches in univariate multiscale sample and dispersion entropy. Entropy, 20(2), 138.