# petersen: Lincoln-Petersen estimator for caribou abundance In caribou: Estimation of caribou abundance based on large scale aggregations monitored by radio telemetry

## Description

The function `petersen` estimates the total population size based on the Lincoln-Petersen Index as applied to radio telemetry data by White and Garrott (1990). It uses the Lincoln-Petersen estimator with Chapman's (1951) bias correction and the bias corrected standard error estimator of Seber (1970) and Wittes (1972).

## Usage

 ```1 2 3 4``` ```petersen(mat, M, S = 0) ## S3 method for class 'petersen' print(x,...) ```

## Arguments

 `mat` A matrix containing in the first column the number of radio-collared animals in the detected (photographed) groups and in the second column the corresponding size of the detected groups. `M` A numeric: the total number of active collars during the census (equivalent to the argument `n` in the function `abundance`). `S` A numeric: the minimum size that define well aggregated groups. Only observations from well aggregated groups (containing at least `S` animals) are taken into account in the computation. The default is zero (every observation is included in the computation). `x` An object, produced by the `petersen` function, to print. `...` Further arguments to be passed to methods (see `print.default`).

## Value

 `G ` The number of well aggregated groups. `R ` The total number of radio-collared animal observed in the well aggregated groups. `C ` The total number of animals observed in the well aggregated groups containing at least one radio-collared animal during the survey. `T.hat ` The modified lincoln-Petersen estimator for the total number of animals in a herd. `se_T.hat ` The estimated standard error of `LP_T.hat`. `mat_aggre ` A matrix containing a subset of the input matrix `mat`: the data for the well aggregated groups only. `call ` The function call (object of class "call").

## Author(s)

Helene Crepeau [email protected] and
Louis-Paul Rivest [email protected] and
Serge Couturier [email protected] and
Sophie Baillargeon [email protected]

## References

Chapman, D. G. (1951). Some properties of the hypergeometric distribution with applications to zoological sample censuses. University of California Publications in Statistics, 1(7), 131-160.

Seber, G.A.F. (1970). The effects of trap response on tag recapture estimates. Biometrics, 26, 13-22.

White, G.C. and Garrott, R.A. (1990). Analysis of wildlife radio-tracking data. San Diego: Academic Press.

Wittes, J.T. (1972). On the bias and estimated variance of Chapman's two-sample capture-recapture population estimate. Biometrics, 28, 592-597.

`abundance`
 ```1 2 3``` ```data(GRH93) petersen(GRH93, M=92) # default S=0 petersen(GRH93, M=92, S=4000) ```