preseqR (version 4.0.0)

bbc.rSAC: BBC estimator

Description

bbc.rSAC predicts the expected number of species represented at least \(r\) times in a random sample, based on the initial sample. The estimator was originally proposed by Boneh et al. (1998) for estimating the SAC. We generalize this estimator for predicting the \(r\)-SAC.

Usage

bbc.rSAC(n, r=1)

Arguments

n

A two-column matrix. The first column is the frequency \(j = 1,2,\dots\); and the second column is \(N_j\), the number of species with each species represented exactly \(j\) times in the initial sample. The first column must be sorted in an ascending order.

r

A positive integer. Default is 1.

Value

The estimator for the \(r\)-SAC. The input of the estimator is a vector of sampling efforts \(t\), i.e., the relative sample sizes comparing with the initial sample. For example, \(t = 2\) means a random sample that is twice the size of the initial sample.

References

Boneh, S., Boneh, A., & Caron, R. J. (1998). Estimating the prediction function and the number of unseen species in sampling with replacement. Journal of the American Statistical Association, 93(441), 372-379.

Deng, C., Daley, T., Calabrese, P., Ren, J., & Smith, A.D. (2016). Estimating the number of species to attain sufficient representation in a random sample. arXiv preprint arXiv:1607.02804v3.

Examples

# NOT RUN {
## load library
library(preseqR)

## import data
data(FisherButterfly)

## construct the estimator for SAC
bbc1 <- bbc.rSAC(FisherButterfly, r=1)
## The number of species represented at least once in a sample, 
## when the sample size is 10 or 20 times of the initial sample
bbc1(c(10, 20))

## construct the estimator for r-SAC
bbc2 <- bbc.rSAC(FisherButterfly, r=2)
## The number of species represented at least twice in a sample, 
## when the sample size is 50 or 100 times of the initial sample
bbc2(c(50, 100))
# }