IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-022-00302-6.html
   My bibliography  Save this article

The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications

Author

Listed:
  • Ahmed Elshahhat

    (Zagazig University)

  • EL-Sayed A. El-Sherpieny

    (Cairo University)

  • Amal S. Hassan

    (Cairo University)

Abstract

A new three-parameter lifetime distribution based on compounding Pareto and Poisson distributions is introduced and discussed. Various statistical and reliability properties of the proposed distribution including: quantiles, ordinary moments, median, mode, quartiles, mean deviations, cumulants, generating functions, entropies, mean residual life, order statistics and stress-strength reliability are obtained. In presence of data collected under Type-II censoring, from frequentist and Bayesian points of view, the model parameters are estimated. Using independent gamma priors, Bayes estimators against the squared-error, linear-exponential and general-entropy loss functions are developed. Based on asymptotic properties of the classical estimators, asymptotic confidence intervals of the unknown parameters are constructed using observed Fisher’s information. Since the Bayes estimators cannot be obtained in closed-form, Markov chain Monte Carlo techniques are considered to approximate the Bayes estimates and to construct the highest posterior density intervals. A Monte Carlo simulation study is conducted to examine the performance of the proposed methods using various choices of effective sample size. To highlight the perspectives of the utility and flexibility of the new distribution, two numerical applications using real engineering data sets are investigated and showed that the proposed model fits well compared to other eleven lifetime models.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00302-6
    DOI: 10.1007/s13171-022-00302-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-022-00302-6
    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/s13171-022-00302-6?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. 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. 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.
    3. Wanbo Lu & Daimin Shi, 2012. "A new compounding life distribution: the Weibull--Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 21-38, March.
    4. Saralees Nadarajah & Vicente Cancho & Edwin Ortega, 2013. "The geometric exponential Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 355-380, August.
    5. 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.
    6. 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.
    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. A. Asgharzadeh & Hassan S. Bakouch & L. Esmaeili, 2013. "Pareto Poisson--Lindley distribution with applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1717-1734, August.
    9. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    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. 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.
    4. 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.
    5. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Shovan Chowdhury, 2014. "Compounded Generalized Weibull Distributions - A Unified Approach," Working papers 148, Indian Institute of Management Kozhikode.
    11. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    12. Eryilmaz, Serkan, 2016. "A new class of lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 63-71.
    13. Saralees Nadarajah & Vicente Cancho & Edwin Ortega, 2013. "The geometric exponential Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 355-380, August.
    14. Ibrahim Elbatal & Emrah Altun & Ahmed Z. Afify & Gamze Ozel, 2019. "The Generalized Burr XII Power Series Distributions with Properties and Applications," Annals of Data Science, Springer, vol. 6(3), pages 571-597, September.
    15. Mahmoudi, Eisa & Jafari, Ali Akbar, 2012. "Generalized exponential–power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4047-4066.
    16. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    17. 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.
    18. Rasool Roozegar & G. G. Hamedani & Leila Amiri & Fatemeh Esfandiyari, 2020. "A New Family of Lifetime Distributions: Theory, Application and Characterizations," Annals of Data Science, Springer, vol. 7(1), pages 109-138, March.
    19. Jimut Bahan Chakrabarty & Shovan Chowdhury, 2016. "Compounded Inverse Weibull Distributions: Properties, Inference and Applications," Working papers 213, Indian Institute of Management Kozhikode.
    20. 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.

    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:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00302-6. 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.