## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 30, Number 1 (2016), 47-69.

### Likelihood-based inference for population size in a capture–recapture experiment with varying probabilities from occasion to occasion

Luis Ernesto Bueno Salasar, José Galvão Leite, and Francisco Louzada

#### Abstract

The estimation of the size of a population is, in general, performed using capture–recapture experiments. In this paper, we consider a closed population capture–recapture model in which individuals are captured independently and with the same probability in each sampling occasion, but the probabilities may vary from occasion to occasion. The unknown number of individuals is the parameter of interest, while the capture probabilities are the nuisance ones. Four likelihood functions free of nuisance parameters, namely the profile, conditional, uniform and Jeffrey’s integrated likelihood functions are derived and procedures for point and interval estimation are discussed. The estimation of population size is illustrated on a real dataset. The frequentist properties of the estimators are evaluated by means of a simulation study. The Jeffrey’s integrated likelihood achieved the best performance over all considered estimators for both point and interval estimation, particularly in situations with little information with small number of elements, small capture probabilities and small number of capture occasions.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 30, Number 1 (2016), 47-69.

**Dates**

Received: June 2013

Accepted: July 2014

First available in Project Euclid: 19 January 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1453211802

**Digital Object Identifier**

doi:10.1214/14-BJPS255

**Mathematical Reviews number (MathSciNet)**

MR3453514

**Zentralblatt MATH identifier**

1381.62029

**Keywords**

Capture–recapture conditional likelihood Jeffrey’s integrated likelihood population size profile likelihood simulation uniform integrated likelihood

#### Citation

Salasar, Luis Ernesto Bueno; Leite, José Galvão; Louzada, Francisco. Likelihood-based inference for population size in a capture–recapture experiment with varying probabilities from occasion to occasion. Braz. J. Probab. Stat. 30 (2016), no. 1, 47--69. doi:10.1214/14-BJPS255. https://projecteuclid.org/euclid.bjps/1453211802