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

In shearer/simboot: Simultaneous Inference for Diversity Indices

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

shearer/simboot documentation built on Feb. 13, 2024, 6:58 a.m.