entropy.ChaoShen {entropy}

Chao-Shen Entropy Estimator

Description

entropy.ChaoShen estimates the Shannon entropy H of the random variable Y from the corresponding observed counts y using the method of Chao and Shen (2003).

Usage

entropy.ChaoShen(y, unit=c("log", "log2", "log10"))

Arguments

y

vector of counts.

unit

the unit in which entropy is measured. The default is "nats" (natural units). For computing entropy in "bits" set unit="log2".

Details

The Chao-Shen entropy estimator (2003) is a Horvitz-Thompson (1952) estimator applied to the problem of entropy estimation, with additional coverage correction as proposed by Good (1953).

Note that the Chao-Shen estimator is not a plug-in estimator, hence there are no explicit underlying bin frequencies.

Value

entropy.ChaoShen returns an estimate of the Shannon entropy.

Author(s)

Korbinian Strimmer (https://strimmerlab.github.io).

References

Chao, A., and T.-J. Shen. 2003. Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample. Environ. Ecol. Stat. 10:429-443.

Good, I. J. 1953. The population frequencies of species and the estimation of population parameters. Biometrika 40:237-264.

Horvitz, D.G., and D. J. Thompson. 1952. A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47:663-685.

See Also

entropy, entropy.shrink, entropy.Dirichlet, entropy.NSB.

Examples

# load entropy library 
library("entropy")

# observed counts for each bin
y = c(4, 2, 3, 0, 2, 4, 0, 0, 2, 1, 1)  

# estimate entropy using Chao-Shen method
entropy.ChaoShen(y)

# compare to empirical estimate
entropy.empirical(y)