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Renyi Entropy

Source: R/eeg-complexity.R
renyiEntropy.Rd

Computes the Renyi entropy of order alpha of a one-dimensional signal (Renyi, 1961) – a one-parameter generalization of the Shannon entropy of the signal's amplitude distribution. The signal is discretized into bins equal-width bins to form a probability distribution \(p\), and \(H_\alpha = \frac{1}{1-\alpha}\ln\left(\sum_i p_i^\alpha\right)\) is returned in nats. Special cases: \(\alpha \to 1\) is the Shannon entropy, \(\alpha = 2\) the collision entropy, and \(\alpha \to \infty\) the min-entropy. \(H_\alpha\) is non-increasing in \(\alpha\).

Usage

renyiEntropy(x, alpha = 2, bins = 16L)

Arguments

x

A numeric vector (the time series).

alpha

Order of the Renyi entropy (default 2, the collision entropy); alpha = 1 returns the Shannon entropy.

bins

Number of equal-width bins for the amplitude histogram (default 16).

Value

A single numeric value, the Renyi entropy in nats.

References

Renyi, A. (1961). "On measures of entropy and information." In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, 547–561.

See also

svdEntropy, petrosianFD, eegComplexity for other complexity measures.

Examples

set.seed(1)
renyiEntropy(rnorm(1000), alpha = 2)   # collision entropy
#> [1] 2.146111
renyiEntropy(rnorm(1000), alpha = 1)   # = Shannon entropy
#> [1] 2.300707