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A note on modelling underreported Poisson counts

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  • Peter Fader
  • Bruce Hardie

Abstract

In this paper we present a parsimonious model for the analysis of underreported Poisson count data. In contrast to previously developed methods, we are able to derive analytic expressions for the key marginal posterior distributions that are of interest. The usefulness of this model is explored via a re-examination of previously analysed data covering the purchasing of port wine (Ramos, 1999).

Suggested Citation

  • Peter Fader & Bruce Hardie, 2000. "A note on modelling underreported Poisson counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 953-964.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:8:p:953-964
    DOI: 10.1080/02664760050173283
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    References listed on IDEAS

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    1. David C. Schmittlein & Albert C. Bemmaor & Donald G. Morrison, 1985. "Technical Note—Why Does the NBD Model Work? Robustness in Representing Product Purchases, Brand Purchases and Imperfectly Recorded Purchases," Marketing Science, INFORMS, vol. 4(3), pages 255-266.
    2. Abel P. Jeuland & Frank M. Bass & Gordon P. Wright, 1980. "A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes," Operations Research, INFORMS, vol. 28(2), pages 255-277, April.
    3. Winkelmann, Rainer, 1996. "Markov Chain Monte Carlo Analysis of Underreported Count Data with an Application to Worker Absenteeism," Empirical Economics, Springer, vol. 21(4), pages 575-587.
    4. van Praag, B M S & Vermeulen, E M, 1993. "A Count-Amount Model with Endogenous Recording of Observations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 383-395, Oct.-Dec..
    5. Francisco Fernando & Ribeiro Ramos, 1999. "Underreporting of purchases of port wine," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 485-494.
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    Cited by:

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    3. Vidhura Tennekoon, 2017. "Counting unreported abortions: A binomial-thinned zero-inflated Poisson model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(2), pages 41-72.
    4. Michael Braun & Peter S. Fader & Eric T. Bradlow & Howard Kunreuther, 2006. "Modeling the "Pseudodeductible" in Insurance Claims Decisions," Management Science, INFORMS, vol. 52(8), pages 1258-1272, August.
    5. Debjit Sengupta & Tathagata Banerjee & Surupa Roy, 2020. "Estimation of Poisson mean with under‐reported counts: a double sampling approach," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 508-535, December.

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