# pPetersen: Hypothesis Testing Using the Petersen Estimator In mbtyers/recapr: Estimating, Testing, and Simulating Abundance in a Mark-Recapture

## Description

Approximates a p-value for a hypothesis test of the Petersen estimator by means of many simulated draws from the null distribution, conditioned on sample sizes.

## Usage

 ```1 2``` ```pPetersen(estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less") ```

## Arguments

 `estN` The estimated abundance. Either this or the number of recaptures (`m2`) must be specified. `nullN` The abundance given by the null hypothesis `n1` Number of individuals captured and marked in the first sample `n2` Number of individuals captured in the second sample `m2` Number of recaptures. Either this or the estimated abundance (`estN`) must be specified. `nsim` Number of simulated values to draw. Defaults to 100000. `alternative` Direction of the alternative hypothesis. Allowed values are `"less"`, `"greater"`, or `"2-sided"`. Defaults to `"less"`.

## Value

An approximate p-value for the specified hypothesis test. If `m2` is specified rather than `estN`, output will be returned as a list with two elements: the estimated abundance and p-value.

## Note

Any Petersen-type estimator (such as this) depends on a set of assumptions:

• The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events

• All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events

• Marking in the first event does not affect probability of recapture in the second event

• Individuals do not lose marks between events

• All marks will be reported in the second event

## Author(s)

Matt Tyers

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```output <- pPetersen(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) abline(v=output\$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pPetersen(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output\$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2) ```