IDEAS home Printed from https://ideas.repec.org/a/spr/aodasc/v11y2024i5d10.1007_s40745-023-00478-0.html
   My bibliography  Save this article

A New Compound Distribution and Its Applications in Over-dispersed Count Data

Author

Listed:
  • Peer Bilal Ahmad

    (Islamic University of Science and Technology)

  • Mohammad Kafeel Wani

    (Islamic University of Science and Technology)

Abstract

Every time variance exceeds mean, over-dispersed models are typically employed. This is the reason that over-dispersed models are such an important aspect of statistical modeling. In this work, the parameter of Poisson distribution is assumed to follow a new lifespan distribution called as Chris-Jerry distribution. The resulting compound distribution is an over-dispersed model known as the Poisson-Chris-Jerry distribution. As a result of deriving a general expression for the r th factorial moment, we acquired the moments about origin and the central moments. In addition to this, moment’s related measurements, generating functions, over-dispersion property, reliability characteristics, recurrence relation for probability, and other statistical qualities, have also been described. For the goal of estimating parameter of the suggested model, the maximum likelihood estimation and method of moment estimation have been addressed. The usefulness of maximum likelihood estimates has also been taken into consideration through a simulation study. We employed four real life data sets, examined the goodness-of-fit test, and considered additional standards such as the Akaike’s information criterion and Bayesian information criterion. The outcomes are compared with several potential models.

Suggested Citation

  • Peer Bilal Ahmad & Mohammad Kafeel Wani, 2024. "A New Compound Distribution and Its Applications in Over-dispersed Count Data," Annals of Data Science, Springer, vol. 11(5), pages 1799-1820, October.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:5:d:10.1007_s40745-023-00478-0
    DOI: 10.1007/s40745-023-00478-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40745-023-00478-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40745-023-00478-0?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. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    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. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    2. Raid Al-Aqtash & Avishek Mallick & G.G. Hamedani & Mahmoud Aldeni, 2021. "On the Gumbel-Burr XII Distribution: Regression and Application," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(6), pages 1-31, December.
    3. Pedro Rafael D Marinho & Rodrigo B Silva & Marcelo Bourguignon & Gauss M Cordeiro & Saralees Nadarajah, 2019. "AdequacyModel: An R package for probability distributions and general purpose optimization," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-30, August.
    4. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    5. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.
    6. Sajid Hussain & Muhammad Sajid Rashid & Mahmood Ul Hassan & Rashid Ahmed, 2022. "The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications," Mathematics, MDPI, vol. 10(9), pages 1-19, April.
    7. Sher B. Chhetri & Alfred A. Akinsete & Gokarna Aryal & Hongwei Long, 2017. "The Kumaraswamy transmuted Pareto distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-24, December.
    8. Rana Muhammad Imran Arshad & Christophe Chesneau & Farrukh Jamal, 2019. "The Odd Gamma Weibull-Geometric Model: Theory and Applications," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    9. Gokarna R. Aryal & Keshav P. Pokhrel & Netra Khanal & Chris P. Tsokos, 2019. "Reliability Models Using the Composite Generalizers of Weibull Distribution," Annals of Data Science, Springer, vol. 6(4), pages 807-829, December.
    10. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    11. Pedro L. Ramos & Francisco Louzada, 2019. "A Distribution for Instantaneous Failures," Stats, MDPI, vol. 2(2), pages 1-12, May.
    12. Srdjan Kadić & Božidar V. Popović & Ali İ. Genç, 2023. "Two Families of Continuous Probability Distributions Generated by the Discrete Lindley Distribution," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    13. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.

    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:aodasc:v:11:y:2024:i:5:d:10.1007_s40745-023-00478-0. 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.