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Population size estimation based upon zero-truncated, one-inflated and sparse count data

Author

Listed:
  • Dankmar Böhning

    (University of Southampton)

  • Herwig Friedl

    (Graz University of Technology)

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.

Suggested Citation

  • Dankmar Böhning & Herwig Friedl, 2021. "Population size estimation based upon zero-truncated, one-inflated and sparse count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1197-1217, October.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-021-00556-8
    DOI: 10.1007/s10260-021-00556-8
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    References listed on IDEAS

    as
    1. Ryan T. Godwin & Dankmar Böhning, 2017. "Estimation of the population size by using the one-inflated positive Poisson model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 425-448, February.
    2. Anne Chao & John Bunge, 2002. "Estimating the Number of Species in a Stochastic Abundance Model," Biometrics, The International Biometric Society, vol. 58(3), pages 531-539, September.
    3. D. J. Venzon & S. H. Moolgavkar, 1988. "A Method for Computing Profile‐Likelihood‐Based Confidence Intervals," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 87-94, March.
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    Cited by:

    1. Mohammad Kafeel Wani & Peer Bilal Ahmad, 2025. "One-Inflated Zero-Truncated Poisson Distribution: Statistical Properties and Real Life Applications," Annals of Data Science, Springer, vol. 12(2), pages 639-666, April.
    2. Yang Liu & Yukun Liu & Pengfei Li & Riquan Zhang, 2024. "Two-step semiparametric empirical likelihood inference from capture–recapture data with missing covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 786-808, September.

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