R: RFA estimator

ds.rSAC {preseqR} | R Documentation

## RFA estimator

### Description

`ds.rSAC` predicts the expected number of species represented at least r times in a random sample, based on the initial sample.

### Usage

    ds.rSAC(n, r=1, mt=20)

### Arguments

`n` | A two-column matrix. The first column is the frequency j = 1,2,…; 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.
`mt` | An positive integer constraining possible rational function approximations. Default is 20.
`r` | A positive integer. Default is 1.

### Details

The estimator is based on an empirical Bayes approach using rational function approximation (RFA), as described in the paper in the references section.

`ds.rSAC` is the fast version of `ds.rSAC.bootstrap`. The function does not provide the confidence interval. To obtain the confidence interval along with the estimates, one should use the function `ds.rSAC.bootstrap`.

### 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.

### Author(s)

Chao Deng

### References

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

    ## load library
    library(preseqR)

    ## import data
    data(FisherButterfly)

    ## construct the estimator for SAC
    ds1 <- ds.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
    ds1(c(10, 20))

    ## construct the estimator for r-SAC
    ds2 <- ds.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
    ds2(c(50, 100))

[Package preseqR version 4.0.0 Index]