Population size estimation based upon zero-truncated, one-inflated and sparse count data: Estimating the number of dice snakes in Graz and flare stars in the Pleiades

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...

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Bibliographic Details
Published in:Statistical methods & applications 2021-10, Vol.30 (4), p.1197-1217
Main Authors: Böhning, Dankmar, Friedl, Herwig
Format: Article
Language:English
Subjects:
Chemistry and Earth Sciences
Computer Science
Economics
Finance
Health Sciences
Humanities
Insurance
Law
Management
Mathematics and Statistics
Medicine
Original Paper
Physics
Statistical Theory and Methods
Statistics
Statistics for Business
Statistics for Engineering
Statistics for Life Sciences
Statistics for Social Sciences
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Summary: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.
ISSN:1618-2510
1613-981X
DOI:10.1007/s10260-021-00556-8