Entropy.z {EntropyEstimation}

Entropy.z

Description

Returns the Z estimator of Shannon's Entropy. This estimator has exponentially decaying bias. See Zhang (2012), Zhang (2013), and Zhang and Grabchak (2014a) for details.

Usage

Entropy.z(x)

Arguments

x

Vector of counts. Must be integer valued. Each entry represents the number of observations of a distinct letter.

Author(s)

Lijuan Cao and Michael Grabchak

References

Z. Zhang (2012). Entropy estimation in Turing's' perspective. Neural Computation 24(5), 1368–1389.

Z. Zhang (2013). Asymptotic normality of an entropy estimator with asymptotically decaying bias. IEEE Transactions on Information Theory 59(1), 504–508.

Z. Zhang and M. Grabchak (2014a). Entropic representation and estimation of diversity indices. http://arxiv.org/abs/1403.3031.

Examples

 x = c(1,3,7,4,8) 
 Entropy.z(x)  
 
 data = rbinom(10,20,.5)
 counts = tabulate(as.factor(data))
 Entropy.z(counts)