IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v8y2017i2d10.1007_s13198-016-0451-1.html
   My bibliography  Save this article

The exponentiated Perks distribution

Author

Listed:
  • Bhupendra Singh

    (Ch. Charan Singh University)

  • Neha Choudhary

    (Ch. Charan Singh University)

Abstract

The study proposes the exponentiated Perks distribution as a generalization of Perks distribution. This generalized distribution provides monotone nondecreasing and bathtub shaped hazard rate function. We study its mathematical properties including mode, median, quantile function and order statistics. The estimation of the model parameters is discussed both in classical and Bayesian setups. The maximum likelihood estimates along with their standard errors and confidence intervals have been obtained. For Bayesian estimation, we use independent gamma priors for the model parameters. The posterior densities of the parameters are simulated using Metropolis–Hastings algorithm to obtain sample-based estimates and highest posterior density intervals. Applications of the proposed distribution to three real data sets have been demonstrated.

Suggested Citation

  • Bhupendra Singh & Neha Choudhary, 2017. "The exponentiated Perks distribution," 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. 8(2), pages 468-478, June.
  • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-016-0451-1
    DOI: 10.1007/s13198-016-0451-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-016-0451-1
    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/s13198-016-0451-1?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. Haberman, Steven & Renshaw, Arthur, 2011. "A comparative study of parametric mortality projection models," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 35-55, January.
    2. Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    3. Richards, S. J., 2008. "Applying Survival Models to Pensioner Mortality Data," British Actuarial Journal, Cambridge University Press, vol. 14(2), pages 257-303, July.
    4. Bhupendra Singh & K. Sharma & Shubhi Rathi & Gajraj Singh, 2012. "A generalized log-normal distribution and its goodness of fit to censored data," Computational Statistics, Springer, vol. 27(1), pages 51-67, 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. S. Nadarajah & S. Bakar, 2013. "A new R package for actuarial survival models," Computational Statistics, Springer, vol. 28(5), pages 2139-2160, October.
    2. Dorota Toczydlowska & Gareth W. Peters & Man Chung Fung & Pavel V. Shevchenko, 2017. "Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components," Risks, MDPI, vol. 5(3), pages 1-77, July.
    3. Karim Barigou & Stéphane Loisel & Yahia Salhi, 2020. "Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect," Risks, MDPI, vol. 9(1), pages 1-18, December.
    4. Ungolo, Francesco & Kleinow, Torsten & Macdonald, Angus S., 2020. "A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 68-84.
    5. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    6. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    7. Mario A. Rojas & Yuri A. Iriarte, 2022. "A Lindley-Type Distribution for Modeling High-Kurtosis Data," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    8. Hunt, Andrew & Villegas, Andrés M., 2015. "Robustness and convergence in the Lee–Carter model with cohort effects," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 186-202.
    9. Ali Doostmoradi, 2018. "A New Distribution with two parameters to Lifetime Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 30-35, September.
    10. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.
    11. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    12. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    13. Kulinskaya, Elena & Gitsels, Lisanne Andra & Bakbergenuly, Ilyas & Wright, Nigel R., 2021. "Dynamic hazards modelling for predictive longevity risk assessment," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 222-231.
    14. Susanna Levantesi & Virginia Pizzorusso, 2019. "Application of Machine Learning to Mortality Modeling and Forecasting," Risks, MDPI, vol. 7(1), pages 1-19, February.
    15. Mitchell, Daniel & Brockett, Patrick & Mendoza-Arriaga, Rafael & Muthuraman, Kumar, 2013. "Modeling and forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 275-285.
    16. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    17. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    18. Jackie Li & Atsuyuki Kogure, 2021. "Bayesian Mixture Modelling for Mortality Projection," Risks, MDPI, vol. 9(4), pages 1-12, April.
    19. Beutner, Eric & Reese, Simon & Urbain, Jean-Pierre, 2017. "Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 117-125.
    20. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2016. "Coherent modeling of male and female mortality using Lee–Carter in a complex number framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 130-137.

    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:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-016-0451-1. 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.