## Abstract

Estimating the size of a hard-to-count population is a challenging matter. In particular, when only few observations of the population to be estimated are available. The matter gets even more complex when one-inflation occurs. This situation is illustrated with the help of two examples: the size of a dice snake population in Graz (Austria) and the number of flare stars in the Pleiades. The paper discusses how one-inflation can be easily handled in likelihood approaches and also discusses how variances and confidence intervals can be obtained by means of a semi-parametric bootstrap. A Bayesian approach is mentioned as well and all approaches result in similar estimates of the hidden size of the population. Finally, a simulation study is provided which shows that the unconditional likelihood approach as well as the Bayesian approach using Jeffreys’ prior perform favorable.

Original language | English |
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Pages (from-to) | 1197-1217 |

Number of pages | 21 |

Journal | Statistical Methods & Applications |

Volume | 30 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 2021 |

## Keywords

- Capture–recapture
- One-inflation
- Zero-truncation

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty