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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
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    Cited by:

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