IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2703-d664066.html
   My bibliography  Save this article

Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

Author

Listed:
  • Ke Wu

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Li Yan

    (School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
    Department of Administrative Sciences, Université du Québec en Outaouais, Gatineau, QC J9A 1L8, Canada)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

Abstract

In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes.

Suggested Citation

  • Ke Wu & Liang Wang & Li Yan & Yuhlong Lio, 2021. "Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2703-:d:664066
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2703/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2703/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emura, Takeshi & Shiu, Shau-Kai, 2014. "Estimation and model selection for left-truncated and right-censored lifetime data with application to electric power transformers analysis," MPRA Paper 57528, University Library of Munich, Germany.
    2. Mu Zhao & Hongmei Jiang & Yong Zhou, 2017. "Estimation of percentile residual life function with left-truncated and right-censored data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(2), pages 995-1006, January.
    3. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    4. Kundu, Debasis & Mitra, Debanjan & Ganguly, Ayon, 2017. "Analysis of left truncated and right censored competing risks data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 12-26.
    5. Sharon Varghese A & V. S. Vaidyanathan, 2020. "Parameter estimation of Lindley step stress model with independent competing risk under type 1 censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(12), pages 3026-3043, June.
    6. Yan Shen & Ancha Xu, 2018. "On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5558-5572, November.
    7. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    8. Kotb, M.S. & Raqab, M.Z., 2017. "Inference and prediction for modified Weibull distribution based on doubly censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 195-207.
    9. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    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. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.

    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. Zhiyuan Zuo & Liang Wang & Yuhlong Lio, 2022. "Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations," Energies, MDPI, vol. 16(1), pages 1-25, December.
    2. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    3. Zhang, Chunfang & Wang, Liang & Bai, Xuchao & Huang, Jianan, 2022. "Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    4. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    5. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    6. Chengping Gong & Chengxiu Ling, 2018. "Robust Estimations for the Tail Index of Weibull-Type Distribution," Risks, MDPI, vol. 6(4), pages 1-15, October.
    7. Jiang, Renyan & Qi, Faqun & Cao, Yu, 2023. "Relation between aging intensity function and WPP plot and its application in reliability modelling," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    8. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    9. Zhang, Fode & Shi, Yimin, 2016. "Geometry of exponential family with competing risks and censored data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 234-245.
    10. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    11. Hanieh Panahi, 2019. "Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data," 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. 10(4), pages 510-518, August.
    12. Kotb, M.S. & Raqab, M.Z., 2019. "Statistical inference for modified Weibull distribution based on progressively type-II censored data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 233-248.
    13. Shuto, Susumu & Amemiya, Takashi, 2022. "Sequential Bayesian inference for Weibull distribution parameters with initial hyperparameter optimization for system reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    14. Ding, Wenzhe & Bai, Xiang & Wang, Qingwei & Long, Fang & Li, Hailin & Wu, Zhengrong & Liu, Jian & Yao, Huisheng & Yang, Hong, 2024. "A truncated test scheme design method for success-failure in-orbit tests," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    15. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    16. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    17. Bee, Marco & Espa, Giuseppe & Giuliani, Diego, 2015. "Approximate maximum likelihood estimation of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 14-26.
    18. Lee, Amy H.I. & Wu, Chien-Wei & Wang, To-Cheng & Kuo, Ming-Han, 2024. "Construction of acceptance sampling schemes for exponential lifetime products with progressive type II right censoring," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    19. Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    20. Mohamed A. W. Mahmoud & Mohamed G. M. Ghazal & Hossam M. M. Radwan, 2023. "Bayesian Estimation and Optimal Censoring of Inverted Generalized Linear Exponential Distribution Using Progressive First Failure Censoring," Annals of Data Science, Springer, vol. 10(2), pages 527-554, April.

    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:9:y:2021:i:21:p:2703-:d:664066. 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.