Hill.sd {EntropyEstimation}

Hill.sd

Description

Returns the estimated asymptotic standard deviation for the Z estimator of Hill's diversity numbe. Note that this is also the asymptotic standard deviation of the plug-in estimator. See Zhang and Grabchak (2014a) for details.

Usage

Hill.sd(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 Hill's deversity numbe. 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)
 Hill.sd(x,2)  
 
 data = rbinom(10,20,.5)
 counts = tabulate(as.factor(data))
 Hill.sd(counts,2)