# Dispersion entropy

`Entropies.dispersion_entropy`

— Function```
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).

**Description**

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.