ztnb.rSAC {preseqR} | R Documentation |
ZTNB estimator
Description
ztnb.rSAC
predicts the expected number of species represented at least
r
times in a random sample, based on the initial sample.
Usage
ztnb.rSAC(n, r=1, size=SIZE.INIT, mu=MU.INIT)
Arguments
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 |
Details
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).
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
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.
See Also
Examples
## 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))