Renyi.z {EntropyEstimation}

Renyi.z

Description

Returns the Z estimator of Renyi's entropy. This is based on taking the log of the Z estimator of Renyi's equivalent entropy and dividing by (1-r). When r=1 returns the Z estimator of Shannon's entropy. See Zhang and Grabchak (2014a) for details.

Usage

Renyi.z(x, r)

Arguments

x

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

r

Order of Renyi's equivalent entropy this index is based on. Must be a strictly positive real number.

Author(s)

Lijuan Cao and Michael Grabchak

References

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)
 Renyi.z(x,2)  
 
 data = rbinom(10,20,.5)
 counts = tabulate(as.factor(data))
 Renyi.z(counts,2)