# rPetersen: Random Draws from the Petersen Estimator In mbtyers/recapr: Estimating, Testing, and Simulating Abundance in a Mark-Recapture

## Description

Returns a vector of random draws from the Petersen estimator in a mark-recapture experiment, given values of the true abundance and the sample size in both events. The function first simulates a vector of recaptures (m2) from a hypergeometric distribution, and then uses these to compute a vector of draws from the estimator.

If capture probabilities (`p1` and/or `p2`) are specified instead of sample size(s), the sample size(s) will first be drawn from a binomial distribution, then the number of recaptures. If both sample size and capture probability are specified for a given sampling event, only the sample size will be used.

## Usage

 `1` ```rPetersen(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL) ```

## Arguments

 `length` The length of the random vector to return. `N` The value of the true abundance. This may be a single number or vector of values equal to `length`. `n1` Number of individuals captured and marked in the first sample. This may be a single number or vector of values equal to `length`. `n2` Number of individuals captured in the second sample. This may be a single number or vector of values equal to `length`. `p1` Alternately, probability of capture in the first sample. This may be a single number or vector of values equal to `length`. `p2` Alternately, probability of capture in the second sample. This may be a single number or vector of values equal to `length`.

## Value

A vector of random draws from the Petersen estimator

## 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``` ```draws <- rPetersen(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete values ```