IDEAS home Printed from https://ideas.repec.org/p/ant/wpaper/2006011.html
   My bibliography  Save this paper

On the sum of independent zero-truncated Poisson random variables

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://repository.uantwerpen.be/docman/irua/b66c5a/4743e891.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lengu, D. & Syntetos, A.A. & Babai, M.Z., 2014. "Spare parts management: Linking distributional assumptions to demand classification," European Journal of Operational Research, Elsevier, vol. 235(3), pages 624-635.
    2. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    3. F R Johnston & E A Shale & S Kapoor & R True & A Sheth, 2011. "Breadth of range and depth of stock: forecasting and inventory management at Euro Car Parts Ltd," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(3), pages 433-441, March.
    4. David R. Bell & Jeongwen Chiang & V. Padmanabhan, 1999. "The Decomposition of Promotional Response: An Empirical Generalization," Marketing Science, INFORMS, vol. 18(4), pages 504-526.
    5. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    6. Fleischmann, Moritz & Kuik, Roelof, 2003. "On optimal inventory control with independent stochastic item returns," European Journal of Operational Research, Elsevier, vol. 151(1), pages 25-37, November.
    7. Tovey C. Bachman & Pamela J. Williams & Kristen M. Cheman & Jeffrey Curtis & Robert Carroll, 2016. "PNG: Effective Inventory Control for Items with Highly Variable Demand," Interfaces, INFORMS, vol. 46(1), pages 18-32, February.
    8. Arnd Huchzermeier & Ananth Iyer & Julia Freiheit, 2002. "The Supply Chain Impact of Smart Customers in a Promotional Environment," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 228-240, November.
    9. Kusum L. Ailawadi & Praveen K. Kopalle & Scott A. Neslin, 2005. "Predicting Competitive Response to a Major Policy Change: Combining Game-Theoretic and Empirical Analyses," Marketing Science, INFORMS, vol. 24(1), pages 12-24, September.
    10. Tian Xia & Richard Sexton, 2010. "Brand or Variety Choices and Periodic Sales as Substitute Instruments for Monopoly Price Discrimination," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 36(4), pages 333-349, June.
    11. Antoine Legrain & Johnathan Patrick, 2022. "Inventory Management Using a Weekly Review ( s , S ) Policy at the Bank of Canada," Interfaces, INFORMS, vol. 52(2), pages 210-225, March.
    12. Sajadieh, Mohsen S. & Larsen, Christian, 2015. "A coordinated manufacturer-retailer model under stochastic demand and production rate," International Journal of Production Economics, Elsevier, vol. 168(C), pages 64-70.
    13. Dehaybe, Henri & Catanzaro, Daniele & Chevalier, Philippe, 2024. "Deep Reinforcement Learning for inventory optimization with non-stationary uncertain demand," European Journal of Operational Research, Elsevier, vol. 314(2), pages 433-445.
    14. Tong Wang & Beril L. Toktay, 2008. "Inventory Management with Advance Demand Information and Flexible Delivery," Management Science, INFORMS, vol. 54(4), pages 716-732, April.
    15. van Lin, Arjen & Gijsbrechts, Els, 2016. "The battle for health and beauty: What drives supermarket and drugstore category-promotion lifts?," International Journal of Research in Marketing, Elsevier, vol. 33(3), pages 557-577.
    16. K. Sudhir, 2001. "Structural Analysis of Manufacturer Pricing in the Presence of a Strategic Retailer," Marketing Science, INFORMS, vol. 20(3), pages 244-264, October.
    17. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 37-53, February.
    18. Chiang, Chi, 2007. "Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale," European Journal of Operational Research, Elsevier, vol. 177(2), pages 872-881, March.
    19. De Moor, Bram J. & Creemers, Stefan & Boute, Robert N., 2023. "Breaking truck dominance in supply chains: Proactive freight consolidation and modal split transport," International Journal of Production Economics, Elsevier, vol. 257(C).
    20. Arindam Banerjee & Tanushri Banerjee, 2017. "Determinants of Analytics Process Adoption in Emerging Economies: Perspectives from the Marketing Domain in India," Vikalpa: The Journal for Decision Makers, , vol. 42(2), pages 95-110, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ant:wpaper:2006011. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joeri Nys (email available below). General contact details of provider: https://edirc.repec.org/data/ftufsbe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.