| ztp.rSAC {preseqR} | R Documentation |
ztp.rSAC predicts the expected number of species represented at least
r times in a random sample, based on the initial sample.
ztp.rSAC(n, r=1)
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. |
r |
A positive integer. Default is 1. |
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.
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
Cohen, A. Clifford. "Estimating the parameter in a conditional Poisson distribution." Biometrics 16, no. 2 (1960): 203-211.
## 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))