SPECIES (version 1.2.0)

jackknife: Jackknife estimator for the species richness

Description

A function implementing the jackknife estimator of the species number by Burnham and Overton 1978 and 1979.

Usage

jackknife(n, k = 5, conf = 0.95)

Value

The function jackknife returns a list of: JackknifeOrder, Nhat, SE and CI.

JackknifeOrder

the jackknife estimator order specified order by the user or determined by the testing procedure.

Nhat

jackknife estimate.

SE

standard error of the jackknife estimate.

CI

confidence interval of the jackknife estimate.

Arguments

n

a matrix or a numerical data frame of two columns. It is also called the “frequency of frequencies” data in literature. The first column is the frequency \(j=1, 2\ldots\); and the second column is \(n_j\), the number of species observed with \(j\) individuals in the sample.

k

a positive integer. k is the specified Jackknife order. The default is k=5. Burnham and Overton 1978 and 1979 provided a testing procedure for the maximum order to be used in this estimator. If the specified order k or default is greater than the order obtained from the testing procedure, the function will automatically use the determined order rather than k. Currently this function only provide jackknife estimate up to order 10.

conf

a positive number \(\le 1\). conf specifies the confidence level for confidence interval. The default is 0.95. conf also specifies the critical value in the sequential test for jackknife order.

Author

Ji-Ping Wang, Department of Statistics, Northwestern University

References

Burnham, K. P., and Overton,W. S. (1978), Estimation of the Size of a Closed Population When Capture Probabilities Vary Among Animals, Biometrika, 65, 625-633.

Burnham, K. P., and Overton,W. S. (1979), Robust Estimation of Population Size When Capture Probabilities Vary Among Animals, Ecology, 60, 927-936.

Examples

library(SPECIES)

##load data from the package, 
## "butterfly" is the famous tterfly data by Fisher 1943.

data(butterfly)
jackknife(butterfly,k=5)