estShannonf {simboot}R Documentation

Estimator for Shannon's index odered by a factorial variable f.

Description

Estimation function for Shannon's index. Internal use in sbdiv for methods rpht, tsht, asht. Sums up species counts in each columns for every treatment group and estimates Shannon's index with bias correction on the resulting vectors of summed up species counts.

HBC^i=H^i+(Si1)/(2Ni)(1(1/p^is))/(12Ni2)((1/p^is)(1/(p^is2)))/(12Ni3);\widehat{HBC}_{i} = \hat{H}_{i} + (S_i -1)/(2N_{i\bullet}) - (1-\sum(1/\hat{p}_{i\bullet s}))/(12N_{i\bullet}^2) - \sum((1/\hat{p}_{i\bullet s})-(1/(\hat{p}_{i\bullet s}^2)))/(12N_{i\bullet}^3);

i=1,...,k;s=1,...,S;pis=j=1nxsjNii=1,...,k;s=1,...,S;p_{i \bullet s}=\frac{\sum_{j=1}^{n}x_{sj}}{N_{i\bullet}};

H^i=(1)s=1S(p^islog(p^is))\hat{H}_i=(-1)\sum_{s=1}^{S}(\hat{p}_{i \bullet s} log(\hat{p}_{i \bullet s}))

Ni=j=1nNijN_{i\bullet}= \sum_{j=1}^{n}N_{ij} Number of observed individuals in treatment ii.

Usage

estShannonf(X, f)

Arguments

X

nn times pp matrix containing species in pp columns and replicates in nn rows.

f

Factor variable containing treatment groups. Must be of length: replicates times treatment groups.

Value

estimate

Estimated Shannon-Wiener index for treatment groups

varest

Estimated variance of Shannon-Wiener index for treatment groups


[Package simboot version 0.2-8 Index]