IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v76y2013i4p543-558.html
   My bibliography  Save this article

Compound weighted Poisson distributions

Author

Listed:
  • Leda Minkova
  • N. Balakrishnan

Abstract

In this paper, we discuss discrete compound distributions, in which the counting distribution is a weighted Poisson distribution. The over- and under-dispersion of these distributions are then discussed by analyzing the Fisher index of dispersion as well as a newly introduced factorial moment to mean measure. Several cases of compounding distributions and weight functions are subsequently examined in detail. Copyright Springer-Verlag 2013

Suggested Citation

  • Leda Minkova & N. Balakrishnan, 2013. "Compound weighted Poisson distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 543-558, May.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:543-558
    DOI: 10.1007/s00184-012-0403-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-012-0403-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-012-0403-y?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. Willmot, Gord, 1986. "Mixed Compound Poisson Distributions," ASTIN Bulletin, Cambridge University Press, vol. 16(S1), pages 59-79, April.
    2. Balakrishnan, N. & Kozubowski, Tomasz J., 2008. "A class of weighted Poisson processes," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2346-2352, October.
    3. M. J. Goovaerts & M. Vandebroeck & R. Kaas, 1986. "Ordering Of Risks And Weighted Compound Distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(4), pages 273-282, December.
    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. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    2. Freud, Thomas & Rodriguez, Pablo M., 2023. "The Bell–Touchard counting process," Applied Mathematics and Computation, Elsevier, vol. 444(C).

    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. Venegas-Martínez, Francisco & Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo, 2015. "Riesgo operativo en el sector salud en Colombia: 2013," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(43), pages 7-36, segundo s.
    2. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    3. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    4. Beghin, Luisa & Macci, Claudio, 2017. "Asymptotic results for a multivariate version of the alternative fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 260-268.
    5. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    6. Chedly Gelin Louzayadio & Rodnellin Onesime Malouata & Michel Diafouka Koukouatikissa, 2021. "A Weighted Poisson Distribution for Underdispersed Count Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 157-157, July.
    7. Roberto Garra & Enzo Orsingher & Federico Polito, 2018. "A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability," Mathematics, MDPI, vol. 6(1), pages 1-10, January.
    8. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
    9. Ján Mačutek & Gejza Wimmer & Michaela Koščová, 2022. "On a Parametrization of Partial-Sums Discrete Probability Distributions," Mathematics, MDPI, vol. 10(14), pages 1-8, July.
    10. Beghin, Luisa & Macci, Claudio, 2013. "Large deviations for fractional Poisson processes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1193-1202.
    11. A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
    12. Korolev, Victor & Zeifman, Alexander, 2021. "Bounds for convergence rate in laws of large numbers for mixed Poisson random sums," Statistics & Probability Letters, Elsevier, vol. 168(C).
    13. Franco-Arbeláez, Luis Ceferino & Franco-Ceballos, Luis Eduardo & Murillo-Gómez, Juan Guillermo & Venegas-Martínez, Francisco, 2015. "Riesgo operativo en el sector salud en Colombia [Operational Risk in the Health Sector in Colombia]," MPRA Paper 63149, University Library of Munich, Germany.
    14. Nobuaki Hoshino, 2005. "Engen's extended negative binomial model revisited," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 369-387, 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:spr:metrik:v:76:y:2013:i:4:p:543-558. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.