ztp.rSAC {preseqR} | R Documentation |
ZTP estimator
Description
ztp.rSAC
predicts the expected number of species represented at least
r
times in a random sample, based on the initial sample.
Usage
ztp.rSAC(n, r=1)
Arguments
n |
A two-column matrix.
The first column is the frequency |
r |
A positive integer. Default is 1. |
Details
The statistical assumption is that for each species the number of individuals
in a sample follows a Poisson distribution. The Poisson rate lambda
is the same among all species. So the random variable X
, which is
the number of species represented x (x > 0) times, follows a zero-truncated
Poisson distribution. The unknown parameters are estimated by
Cohen (1960). Based on the estimated distribution,
we calculate the expected number of species in a random sample.
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
Cohen, A. Clifford. "Estimating the parameter in a conditional Poisson distribution." Biometrics 16, no. 2 (1960): 203-211.
Examples
## load library
library(preseqR)
## import data
data(FisherButterfly)
## construct the estimator for SAC
ztp1 <- ztp.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
ztp1(c(10, 20))
## construct the estimator for r-SAC
ztp2 <- ztp.rSAC(FisherButterfly, r=2)
## The number of species represented at least once in a sample,
## when the sample size is 10 or 20 times of the initial sample
ztp2(c(50, 100))