IDEAS home Printed from https://ideas.repec.org/a/spr/aodasc/v12y2025i3d10.1007_s40745-024-00554-z.html
   My bibliography  Save this article

Analyzing Insurance Data with an Alpha Power Transformed Exponential Poisson Model

Author

Listed:
  • Mohammed A. Meraou

    (University of Djillali Liabes)

  • Mohammad Z. Raqab

    (Kuwait University
    The University of Jordan)

  • Fatmah B. Almathkour

    (Kuwait University)

Abstract

In this paper, we propose a new model by adding an additional parameter to the baseline distributions for modeling claim and risk data used in actuarial and financial studies. The new model is called alpha power transformed exponential Poisson model. It has three parameters and its probability density function can be skewed and unimodal. Several distributional properties of the proposed model such as reliability, hazard rate, quantile and moments are established. Estimation of the unknown parameters based on maximum likelihood estimation are derived and risk measures such as value at risk and tail value at risk are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Finally, two real data sets of insurance losses are analyzed to check the potential of the proposed model among some of the existing models.

Suggested Citation

  • Mohammed A. Meraou & Mohammad Z. Raqab & Fatmah B. Almathkour, 2025. "Analyzing Insurance Data with an Alpha Power Transformed Exponential Poisson Model," Annals of Data Science, Springer, vol. 12(3), pages 991-1011, June.
    • Handle: RePEc:spr:aodasc:v:12:y:2025:i:3:d:10.1007_s40745-024-00554-z
    DOI: 10.1007/s40745-024-00554-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40745-024-00554-z
    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/s40745-024-00554-z?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. Bettina Grün & Tatjana Miljkovic, 2019. "Extending composite loss models using a general framework of advanced computational tools," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(8), pages 642-660, September.
    2. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    3. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    4. Giovani Carrara Rodrigues & Francisco Louzada & Pedro Luiz Ramos, 2018. "Poisson–exponential distribution: different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 128-144, January.
    5. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
    6. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    7. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    8. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    9. M. Nassar & A. Alzaatreh & M. Mead & O. Abo-Kasem, 2017. "Alpha power Weibull distribution: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10236-10252, October.
    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. 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.
    2. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    3. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    4. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    5. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    6. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.
    7. Mahmoudi, Eisa & Sepahdar, Afsaneh, 2013. "Exponentiated Weibull–Poisson distribution: Model, properties and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 76-97.
    8. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    9. Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2018. "Bayesian inference for Poisson-inverse exponential distribution under progressive type-II censoring with binomial removal," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1235-1249, December.
    10. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    11. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    12. Ahmed Elshahhat & EL-Sayed A. El-Sherpieny & Amal S. Hassan, 2023. "The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1058-1099, February.
    13. Ausaina Niyomdecha & Patchanok Srisuradetchai, 2023. "Complementary Gamma Zero-Truncated Poisson Distribution and Its Application," Mathematics, MDPI, vol. 11(11), pages 1-13, June.
    14. Shumaila Ihtisham & Alamgir Khalil & Sadaf Manzoor & Sajjad Ahmad Khan & Amjad Ali, 2019. "Alpha-Power Pareto distribution: Its properties and applications," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-15, June.
    15. Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    16. 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.
    17. Sanku Dey & Indranil Ghosh & Devendra Kumar, 2019. "Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data," Annals of Data Science, Springer, vol. 6(4), pages 623-650, December.
    18. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    19. Idika Eke Okorie & Anthony Chukwudi Akpanta & Johnson Ohakwe & David Chidi Chikezie & Chris Uche Onyemachi & Manoj Kumar Rastogi, 2021. "Zero-Truncated Poisson-Power Function Distribution," Annals of Data Science, Springer, vol. 8(1), pages 107-129, March.
    20. Jemilohun Vincent Gbenga & Ipinyomi Reuben Adeyemi, 2022. "Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-10, 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:spr:aodasc:v:12:y:2025:i:3:d:10.1007_s40745-024-00554-z. 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.