R: Chao-Shen Entropy Estimator

entropy.ChaoShen {entropy} | R Documentation

## 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 (http://strimmerlab.org).

### 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)

[Package entropy version 1.2.1 Index]