Description Usage Arguments Details Value Author(s) References See Also Examples

`ztnb.rSAC`

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

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

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

`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 |

The statistical assumption is that for each species the number of individuals
in a sample follows a Poisson distribution. The Poisson rate `lambda`

are numbers generated from a gamma distribution. So the random variable
`X`

, which is the number of species represented x (x > 0) times in the
sample, follows a zero-truncated negative binomial distribution. The
unknown parameters are estimated by the function `preseqR.ztnb.em`

based
on the initial sample. Using the estimated distribution, we calculate the
expected number of species represented at least r times in a random sample.
Details of the estimation procedure can be found in the supplement of
Daley T. and Smith AD. (2013).

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

Daley, T., & Smith, A. D. (2013). Predicting the molecular complexity of sequencing libraries. Nature methods, 10(4), 325-327.

Deng C, Daley T & Smith AD (2015). Applications of species accumulation curves in large-scale biological data analysis. Quantitative Biology, 3(3), 135-144.

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
ztnb1 <- ztnb.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
ztnb1(c(10, 20))
## construct the estimator for r-SAC
ztnb2 <- ztnb.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
ztnb2(c(50, 100))
``` |

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