IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v19y2017i2d10.1007_s11009-016-9514-7.html
   My bibliography  Save this article

On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data

Author

Listed:
  • M. Noori Asl

    (University of Tabriz)

  • R. Arabi Belaghi

    (University of Tabriz)

  • H. Bevrani

    (University of Tabriz)

Abstract

In the current paper, based on progressive type-II hybrid censored samples, the maximum likelihood and Bayes estimates for the two parameter Burr XII distribution are obtained. We propose the use of expectation-maximization (EM) algorithm to compute the maximum likelihood estimates (MLEs) of model parameters. Further, we derive the asymptotic variance-covariance matrix of the MLEs by applying the missing information principle and it can be utilized to construct asymptotic confidence intervals (CIs) for the parameters. The Bayes estimates of the unknown parameters are obtained under the assumption of gamma priors by using Lindley’s approximation and Markov chain Monte Carlo (MCMC) technique. Also, MCMC samples are used to construct the highest posterior density (HPD) credible intervals. Simulation study is conducted to investigate the accuracy of the estimates and compare the performance of CIs obtained. Finally, one real data set is analyzed for illustrative purposes.

Suggested Citation

  • M. Noori Asl & R. Arabi Belaghi & H. Bevrani, 2017. "On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 665-683, June.
  • Handle: RePEc:spr:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9514-7
    DOI: 10.1007/s11009-016-9514-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9514-7
    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/s11009-016-9514-7?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. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    2. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    3. Manoj Rastogi & Yogesh Tripathi, 2013. "Inference on unknown parameters of a Burr distribution under hybrid censoring," Statistical Papers, Springer, vol. 54(3), pages 619-643, August.
    4. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.

    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. Rastogi, Manoj Kumar & Tripathi, Yogesh Mani, 2013. "Estimation using hybrid censored data from a two-parameter distribution with bathtub shape," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 268-281.
    2. Manoj Rastogi & Yogesh Tripathi, 2013. "Inference on unknown parameters of a Burr distribution under hybrid censoring," Statistical Papers, Springer, vol. 54(3), pages 619-643, August.
    3. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    4. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.
    5. Lin, Chien-Tai & Chou, Cheng-Chieh & Huang, Yen-Lung, 2012. "Inference for the Weibull distribution with progressive hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 451-467.
    6. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    7. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
    8. Amit Singh Nayal & Bhupendra Singh & Vrijesh Tripathi & Abhishek Tyagi, 2024. "Analyzing stress-strength reliability $$\delta =\text{ P }[U," 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. 15(6), pages 2453-2472, June.
    9. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
    10. Park, Sangun & Ng, Hon Keung Tony & Chan, Ping Shing, 2015. "On the Fisher information and design of a flexible progressive censored experiment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 142-149.
    11. 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.
    12. Balakrishnan, N. & Saleh, H.M., 2011. "Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2775-2792, October.
    13. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    14. Park, Sangun & Balakrishnan, N. & Zheng, Gang, 2008. "Fisher information in hybrid censored data," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2781-2786, November.
    15. Altındağ, Ömer & Aydoğdu, Halil, 2021. "Estimation of renewal function under progressively censored data and its applications," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    16. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    17. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    18. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2015. "Estimation for mixed exponential distributions under type-II progressively hybrid censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 85-96.
    19. Valiollahi, R. & Raqab, Mohammad Z. & Asgharzadeh, A. & Alqallaf, F.A., 2018. "Estimation and prediction for power Lindley distribution under progressively type II right censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 32-47.
    20. M. M. Mohie El-Din & M. Nagy & M. H. Abu-Moussa, 2019. "Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data," Annals of Data Science, Springer, vol. 6(4), pages 673-705, December.

    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:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9514-7. 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.