# ciBailey: Confidence Intervals for the Bailey Estimator In mbtyers/recapr: Estimating, Testing, and Simulating Abundance in a Mark-Recapture

## Description

Calculates approximate confidence intervals(s) for the Bailey estimator, using bootstrapping, the Normal approximation, or both.

The bootstrap interval is created by resampling the data in the second sampling event, with replacement; that is, drawing bootstrap values of m2 from a binomial distribution with probability parameter m2/n2. This technique has been shown to better approximate the distribution of the abundance estimator. Resulting CI endpoints both have larger values than those calculated from a normal distribution, but this better captures the positive skew of the estimator. Coverage has been investigated by means of simulation under numerous scenarios and has consistently outperformed the normal interval. The user is welcomed to investigate the coverage under relevant scenarios.

## Usage

 `1` ```ciBailey(n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000) ```

## Arguments

 `n1` Number of individuals captured and marked in the first sample `n2` Number of individuals captured in the second sample `m2` Number of marked individuals recaptured in the second sample `conf` The confidence level of the desired intervals. Defaults to 0.95. `method` Which method of confidence interval to return. Allowed values are `"norm"`, `"boot"`, or `"both"`. Defaults to `"both"`. `bootreps` Number of bootstrap replicates to use. Defaults to 10000.

## Value

A list with the abundance estimate and confidence interval bounds for the normal-distribution and/or bootstrap confidence intervals.

## 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` ```ciBailey(n1=100, n2=100, m2=20) ```