estShannonWY {simboot}R Documentation

Estimator for Shannon's index row wise.

Description

Estimation function for Shannon's index. Internal use in WYht. Calculates Shannon-Wiener index with bias correction

HBC^ij=H^ij+(Sij1)/(2Nij)(1s=1S(1/p^ijs))/(12Nij2)s=1S((1/p^ijs)(1/(p^ijs2)))/(12Nij3);\widehat{HBC}_{ij} = \hat{H}_{ij} + (S_{ij} -1)/(2N_{ij}) - (1-\sum_{s=1}^{S}(1/\hat{p}_{ijs}))/(12N_{ij}^2) - \sum_{s=1}^{S}((1/\hat{p}_{ijs})-(1/(\hat{p}_{ijs}^2)))/(12N_{ij}^3);

H^ij=(1)s=1S(p^ijslog(p^ijs))\hat{H}_{ij}=(-1)\sum_{s=1}^{S}(\hat{p}_{ijs} log(\hat{p}_{ijs}))

i=1,...,k;j=1,...,n;s=1,...,S;i=1,...,k;j=1,...,n;s=1,...,S;

Sj=S_j = Number of observed species in replicate jj;

Nj=N_j= Number of observed individuals in replicate jj

for every row in a n×pn \times p matrix.

Usage

estShannonWY(x)

Arguments

x

Vector of pp numerical species counts.

Value

Shannon-Wiener index with bias correction


[Package simboot version 0.2-8 Index]