EntropyEstimation (version 1.2.1)

GenSimp.z: GenSimp.z

Description

Returns the Z estimator of the generalized Simpson's index of order r, i.e. of the index sum_k p_k(1-p_k)^r. See Zhang and Zhou (2010) and Zhang and Grabchak (2014a) for details.

Usage

GenSimp.z(x,r)

Arguments

x

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

r

Positive integer representing the order of the generalized Simpson's index. If a noninteger value is given then the integer part is taken. Must be strictly less than sum(x).

Author

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.

Z. Zhang and J. Zhou (2010). Re-parameterization of multinomial distributions and diversity indices. Journal of Statistical Planning and Inference 140(7), 1731-1738.

Examples

 x = c(1,3,7,4,8) 
 GenSimp.z(x,2)  
 
 data = rbinom(10,20,.5)
 counts = tabulate(as.factor(data))
 GenSimp.z(counts,2)