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General flation models for count data

Author

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  • Dankmar Böhning

    (University of Southampton)

  • Helen E. Ogden

    (University of Southampton)

Abstract

The paper discusses very general extensions to existing inflation models for discrete random variables, allowing an arbitrary set of points in the sample space to be either inflated or deflated relative to a baseline distribution. The term flation is introduced to cover either inflation or deflation of counts. Examples include one-inflated count models where the baseline distribution is zero-truncated and count models for data with a few unusual large values. The main result is that inference about the baseline distribution can be based solely on the truncated distribution which arises when the entire set of flation points is truncated. A major application of this result relates to estimating the size of a hidden target population, and examples are provided to illustrate our findings.

Suggested Citation

  • Dankmar Böhning & Helen E. Ogden, 2021. "General flation models for count data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 245-261, February.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:2:d:10.1007_s00184-020-00786-y
    DOI: 10.1007/s00184-020-00786-y
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    References listed on IDEAS

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    1. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
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    Cited by:

    1. Dankmar Böhning & Rattana Lerdsuwansri & Patarawan Sangnawakij, 2023. "Modeling COVID‐19 contact‐tracing using the ratio regression capture–recapture approach," Biometrics, The International Biometric Society, vol. 79(4), pages 3818-3830, December.

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