IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v181y2022ics0167715221002261.html
   My bibliography  Save this article

When is the Conway–Maxwell–Poisson distribution infinitely divisible?

Author

Listed:
  • Geng, Xi
  • Xia, Aihua

Abstract

An essential characteristic for a distribution to play a central role in limit theory is infinite divisibility. In this note, we prove that the Conway–Maxwell–Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or geometric distribution. This explains that, despite its applications in a wide range of fields, there is no theoretical foundation for the CMP distribution to be a natural candidate for the law of small numbers.

Suggested Citation

  • Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002261
    DOI: 10.1016/j.spl.2021.109264
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221002261
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109264?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    2. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107028333.
    3. Kimberly F. Sellers & Sharad Borle & Galit Shmueli, 2012. "The COM‐Poisson model for count data: a survey of methods and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(2), pages 104-116, March.
    4. Bo Li & Huiming Zhang & Jiao He, 2020. "Some characterizations and properties of COM-Poisson random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1311-1329, March.
    5. Subrata Chakraborty & Tomoaki Imoto, 2016. "Extended Conway-Maxwell-Poisson distribution and its properties and applications," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-19, December.
    6. Tammy Harris & Joseph M. Hilbe & James W. Hardin, 2014. "Modeling count data with generalized distributions," Stata Journal, StataCorp LP, vol. 14(3), pages 562-579, September.
    7. Li Zhu & Kimberly F. Sellers & Darcy Steeg Morris & Galit Shmueli, 2017. "Bridging the Gap: A Generalized Stochastic Process for Count Data," The American Statistician, Taylor & Francis Journals, vol. 71(1), pages 71-80, January.
    Full references (including those not matched with items on IDEAS)

    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. Wu, Jiang & Ou, Guiyan & Liu, Xiaohui & Dong, Ke, 2022. "How does academic education background affect top researchers’ performance? Evidence from the field of artificial intelligence," Journal of Informetrics, Elsevier, vol. 16(2).
    2. de Rezende, Rafael & Egert, Katharina & Marin, Ignacio & Thompson, Guilherme, 2022. "A white-boxed ISSM approach to estimate uncertainty distributions of Walmart sales," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1460-1467.
    3. Andries, Petra & Hünermund, Paul, 2020. "Firm-level effects of staged investments in innovation: The moderating role of resource availability," Research Policy, Elsevier, vol. 49(7).
    4. Lin, Jun-You, 2017. "Balancing industry collaboration and academic innovation: The contingent role of collaboration-specific attributes," Technological Forecasting and Social Change, Elsevier, vol. 123(C), pages 216-228.
    5. Di Novi, Cinzia & Leporatti, Lucia & Levaggi, Rosella & Montefiori, Marcello, 2022. "Adherence during COVID-19: The role of aging and socio-economics status in shaping drug utilization," Journal of Economic Behavior & Organization, Elsevier, vol. 204(C), pages 1-14.
    6. Hu, Feng & Bijmolt, Tammo H.A. & Huizingh, Eelko K.R.E., 2020. "The impact of innovation contest briefs on the quality of solvers and solutions," Technovation, Elsevier, vol. 90.
    7. Sinclair, Michael & Ghermandi, Andrea & Signorello, Giovanni & Giuffrida, Laura & De Salvo, Maria, 2022. "Valuing Recreation in Italy's Protected Areas Using Spatial Big Data," Ecological Economics, Elsevier, vol. 200(C).
    8. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.
    9. Hilbe, Joseph M., 2015. "The New Statistics with R: An Introduction for Biologists," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(b01).
    10. Corona Francisco & Wiper Michael Peter & Horrillo Juan de Dios Tena, 2017. "On the importance of the probabilistic model in identifying the most decisive games in a tournament," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 13(1), pages 11-23, March.
    11. Molnár, D. László & Hollósné Marosi, Judit, 2015. "Az öregségi nyugdíjasok halandósága. A nyugellátási összeg, a nyugdíjazási életkor és a halandóság összefüggései Magyarországon, 2004-2012 [Mortality of old-age pensioners. Association among the am," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1258-1290.
    12. Escario, José-Julián & Giménez-Nadal, J. Ignacio & Wilkinson, Anna V., 2022. "Predictors of adolescent truancy: The importance of cyberbullying, peer behavior, and parenting style," Children and Youth Services Review, Elsevier, vol. 143(C).
    13. Requena, Miguel & Reher, David Sven, 2023. "Intergenerational transmission of fertility in Spain among cohorts born during the first half of twentieth century," Economics & Human Biology, Elsevier, vol. 50(C).
    14. Vigren, Andreas, 2018. "How many want to drive the bus? Analyzing the number of bids for public transport bus contracts," Transport Policy, Elsevier, vol. 72(C), pages 138-147.
    15. Lindahl, Jonas, 2023. "Conscientiousness predicts doctoral students’ research productivity," Journal of Informetrics, Elsevier, vol. 17(1).
    16. Seng Huat Ong & Shin Zhu Sim & Shuangzhe Liu & Hari M. Srivastava, 2023. "A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data," Stats, MDPI, vol. 6(3), pages 1-14, September.
    17. Putzhammer, Moritz & Slangen, Arjen & Puck, Jonas & Lindner, Thomas, 2020. "Multinational firms' pace of expansion within host countries: How high rates of pro-market reform hamper the local exploitation of foreign expansion knowledge," Journal of International Management, Elsevier, vol. 26(1).
    18. Sun, Xiaochi & Cui, Xuebin & Sun, Yacheng, 2023. "Understanding the sequential interdependence of mobile app adoption within and across categories," International Journal of Research in Marketing, Elsevier, vol. 40(3), pages 659-678.
    19. Lall, Ashish, 2018. "Delays in the New York City metroplex," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PA), pages 139-153.
    20. Subash Sasidharan & M. Padmaja, 2018. "Do Financing Constraints Impact Outward Foreign Direct Investment? Evidence from India," Asian Development Review, MIT Press, vol. 35(1), pages 108-132, March.

    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:eee:stapro:v:181:y:2022:i:c:s0167715221002261. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.