simboot (version 0.2-0)

estShannonf: 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. $$\widehat{HBC}_{i} = \hat{H}_{i} + (S_i -1)/(2N_{i\bullet}) - (1-\sum(1/\hat{p}_{i\bullet s}))/(12N_{i\bullet}^2) - \sum((1/\hat{p}_{i\bullet s})-(1/(\hat{p}_{i\bullet s}^2)))/(12N_{i\bullet}^3);$$

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

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

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

Usage

estShannonf(X, f)

Arguments

X

$n$ times $p$ matrix containing species in $p$ columns and replicates in $n$ 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