| ztpois.mincount {preseqR} | R Documentation |
The function estimates the expected number of species represented at least r times in a random sample based on the initial sample using zero truncated Poisson distributino.
ztpois.mincount(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 j times in the initial sample. The first column must be sorted in an ascending order. |
r |
A vector of positive integers. 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 constructed estimator for the number of species represneted at least r times in a sample. 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 the sample is twice the size of the initial sample.
Chao Deng
Cohen Jr, A. C. (1960). Estimating the parameters of a modified Poisson distribution. Journal of the American Statistical Association, 55(289), 139-143.
## load library library(preseqR) ## import data data(FisherButterflyHist) ## construct the estimator for the number of species ## represented at least once, twice or three times in a sample ztpois.estimator <- ztpois.mincount(FisherButterflyHist, r=1:3) ## The number of species represented at least once, twice or three times ## when the sample size is 10 or 20 times of the initial sample ztpois.estimator(c(10, 20))