GenSimp.sd: GenSimp.sd

In EntropyEstimation: Estimation of Entropy and Related Quantities

Description

Returns the estimated asymptotic standard deviation of 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. This estimate of the standard deviation is based on the formula in Zhang and Grabchak (2014a) and not the one in Zhang and Zhou (2010).

Usage

GenSimp.sd(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(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.

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

EntropyEstimation documentation built on May 1, 2019, 6:33 p.m.