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On the sum of independent zero-truncated Poisson random variables

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  • SPRINGAEL, Johan
  • VAN NIEUWENHUYSE, Inneke

Abstract

The objective of this article is to derive the density function and cumulative distribution function for random variables which may be written as the sum of independent (either identical or non-identical) zerotruncated Poisson random variables. The obtained expressions may be particularly useful for modelling purposes, especially in view of linking common purchase quantity models from the marketing literature to stochastic production-inventory models from the operations management literature.

Suggested Citation

  • SPRINGAEL, Johan & VAN NIEUWENHUYSE, Inneke, 2006. "On the sum of independent zero-truncated Poisson random variables," Working Papers 2006011, University of Antwerp, Faculty of Business and Economics.
    • Handle: RePEc:ant:wpaper:2006011
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    File URL: https://repository.uantwerpen.be/docman/irua/b66c5a/4743e891.pdf
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    References listed on IDEAS

    as
    1. Dominey, M. J. G. & Hill, R. M., 2004. "Performance of approximations for compound Poisson distributed demand in the newsboy problem," International Journal of Production Economics, Elsevier, vol. 92(2), pages 145-155, November.
    2. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    3. Matheus, Peter & Gelders, Ludo, 2000. "The (R, Q) inventory policy subject to a compound Poisson demand pattern," International Journal of Production Economics, Elsevier, vol. 68(3), pages 307-317, December.
    4. Jorge M. Silva-Risso & Randolph E. Bucklin & Donald G. Morrison, 1999. "A Decision Support System for Planning Manufacturers' Sales Promotion Calendars," Marketing Science, INFORMS, vol. 18(3), pages 274-300.
    5. Hill, Roger M. & Johansen, Soren Glud, 2006. "Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding," European Journal of Operational Research, Elsevier, vol. 169(1), pages 111-132, February.
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    Cited by:

    1. Guo-Liang Tian & Xiqian Ding & Yin Liu & Man-Lai Tang, 2019. "Some new statistical methods for a class of zero-truncated discrete distributions with applications," Computational Statistics, Springer, vol. 34(3), pages 1393-1426, September.
    2. Yixuan Zou & Jan Hannig & Derek S. Young, 2021. "Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.

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