Description Usage Arguments Details Value Author(s) References Examples

`preseqR.rSAC`

predicts the expected number of species represented at least
*r* times in a random sample based on the initial sample.

1 | ```
preseqR.rSAC(n, r=1, mt=20, size=SIZE.INIT, mu=MU.INIT)
``` |

`n` |
A two-column matrix.
The first column is the frequency |

`mt` |
A positive integer constraining possible rational function approximations. Default is 20. |

`r` |
A positive integer. Default is 1. |

`size` |
A positive double, the initial value of the parameter |

`mu` |
A positive double, the initial value of the parameter |

`preseqR.rSAC`

combines the nonparametric approach using the rational
function approximation and the parametric approach using the
zero-truncated negative binomial (ZTNB). For a given initial sample, if the sample
is from a heterogeneous population, the function calls
`ds.rSAC`

; otherwise it calls `ztnb.rSAC`

. The degree
of heterogeneity is measured by the coefficient of variation, which is
estimated by the ZTNB approach.

`preseqR.rSAC`

is the fast version of `preseqR.rSAC.bootstrap`

.
The function does not provide the confidence interval. To obtain the
confidence interval along with the estimates, one should use the function
`preseqR.rSAC.bootstrap`

.

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.

Chao Deng

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
## load library
library(preseqR)
## import data
data(FisherButterfly)
## construct the estimator for SAC
estimator1 <- preseqR.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
estimator1(c(10, 20))
## construct the estimator for r-SAC
estimator2 <- preseqR.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
estimator2(c(50, 100))
``` |

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