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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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    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).
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    Cited by:

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