IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1122-d1078397.html
   My bibliography  Save this article

A Flexible Semi-Poisson Distribution with Applications to Insurance Claims and Biological Data

Author

Listed:
  • Fatimah E. Almuhayfith

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia)

  • Sudeep R. Bapat

    (Department of Operations Management and Quantitative Techniques, Indian Institute of Management, Indore 453556, India)

  • Hassan S. Bakouch

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • Aminh M. Alnaghmosh

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia)

Abstract

In this paper, a discrete one-parameter distribution called the semi-Poisson distribution is introduced, which is based on a set of non-negative integers. It is seen that this distribution captures over-dispersion and zero-inflation scenarios well. A few properties of the proposed distribution, such as moments, the probability-generating function, index of dispersion, recurrence relation for the moments, and negative moments are presented. The distribution is applied to two real-life datasets related to insurance claims and parasite counts, where it is noted to perform better than many of the existing discrete distributions based on Z + , including some of the recently introduced ones.

Suggested Citation

  • Fatimah E. Almuhayfith & Sudeep R. Bapat & Hassan S. Bakouch & Aminh M. Alnaghmosh, 2023. "A Flexible Semi-Poisson Distribution with Applications to Insurance Claims and Biological Data," Mathematics, MDPI, vol. 11(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1122-:d:1078397
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1122/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1122/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    2. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    3. 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.
    4. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Deepesh Bhati & Hassan S. Bakouch, 2019. "A new infinitely divisible discrete distribution with applications to count data modeling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(6), pages 1401-1416, March.
    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. L. Elbakidze & Y. H. Jin, 2015. "Are Economic Development and Education Improvement Associated with Participation in Transnational Terrorism?," Risk Analysis, John Wiley & Sons, vol. 35(8), pages 1520-1535, August.
    2. Abbas Moghimbeigi & Mohammed Reza Eshraghian & Kazem Mohammad & Brian Mcardle, 2008. "Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1193-1202.
    3. Moghimbeigi, Abbas & Eshraghian, Mohammad Reza & Mohammad, Kazem & McArdle, Brian, 2009. "A score test for zero-inflation in multilevel count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1239-1248, February.
    4. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    5. Christopher J. W. Zorn, 1998. "An Analytic and Empirical Examination of Zero-Inflated and Hurdle Poisson Specifications," Sociological Methods & Research, , vol. 26(3), pages 368-400, February.
    6. Daniel Biftu Bekalo & Dufera Tejjeba Kebede, 2021. "Zero-Inflated Models for Count Data: An Application to Number of Antenatal Care Service Visits," Annals of Data Science, Springer, vol. 8(4), pages 683-708, December.
    7. Tousifur Rahman & Partha Jyoti Hazarika & M. Masoom Ali & Manash Pratim Barman, 2022. "Three-Inflated Poisson Distribution and its Application in Suicide Cases of India During Covid-19 Pandemic," Annals of Data Science, Springer, vol. 9(5), pages 1103-1127, October.
    8. Moritz Berger & Gerhard Tutz, 2021. "Transition models for count data: a flexible alternative to fixed distribution models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1259-1283, October.
    9. Guillaume Daudin & Elizaveta Archanskaia, 2012. "Heterogeneity and distance puzzle," Working Papers hal-01073683, HAL.
    10. R. Martínez-Espiñeira, 2007. "‘Adopt a Hypothetical Pup’: A Count Data Approach to the Valuation of Wildlife," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(2), pages 335-360, June.
    11. Edgar Ventura Neyra & Gabriel Rodríguez, 2015. "Explaining the Determinants of the Frequency of Exchange Rate Interventions in Peru Using Count Models," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot GmbH, Berlin, vol. 61(3), pages 261-292.
    12. William Greene & Mark N. Harris & Preety Srivastava & Xueyan Zhao, 2018. "Misreporting and econometric modelling of zeros in survey data on social bads: An application to cannabis consumption," Health Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 372-389, February.
    13. Harris, Mark N. & Zhao, Xueyan, 2007. "A zero-inflated ordered probit model, with an application to modelling tobacco consumption," Journal of Econometrics, Elsevier, vol. 141(2), pages 1073-1099, December.
    14. repec:spo:wpmain:info:hdl:2441/53r60a8s3kup1vc9ji21mi9p3 is not listed on IDEAS
    15. Martijn Burger & Frank van Oort & Gert-Jan Linders, 2009. "On the Specification of the Gravity Model of Trade: Zeros, Excess Zeros and Zero-inflated Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(2), pages 167-190.
    16. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    17. Buczkowska, Sabina & de Lapparent, Matthieu, 2014. "Location choices of newly created establishments: Spatial patterns at the aggregate level," Regional Science and Urban Economics, Elsevier, vol. 48(C), pages 68-81.
    18. repec:wsr:wpaper:y:2012:i:095 is not listed on IDEAS
    19. Josep‐Maria Arauzo‐Carod & Daniel Liviano‐Solis & Miguel Manjón‐Antolín, 2010. "Empirical Studies In Industrial Location: An Assessment Of Their Methods And Results," Journal of Regional Science, Wiley Blackwell, vol. 50(3), pages 685-711, August.
    20. K. F. Lam & Hongqi Xue & Yin Bun Cheung, 2006. "Semiparametric Analysis of Zero-Inflated Count Data," Biometrics, The International Biometric Society, vol. 62(4), pages 996-1003, December.
    21. Markus Jochmann, 2013. "What belongs where? Variable selection for zero-inflated count models with an application to the demand for health care," Computational Statistics, Springer, vol. 28(5), pages 1947-1964, October.
    22. Garcia, Serge & Jacob, Julien, 2010. "La valeur récréative de la forêt en France : une approche par les coûts de déplacement," Review of Agricultural and Environmental Studies - Revue d'Etudes en Agriculture et Environnement (RAEStud), Institut National de la Recherche Agronomique (INRA), vol. 91(1).

    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:gam:jmathe:v:11:y:2023:i:5:p:1122-:d:1078397. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.