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Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution

Author

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  • Hare Krishna

    (Ch. Charan Singh University)

  • Rajni Goel

    (Chandigarh University)

Abstract

The formal random censoring plan has been extensively studied earlier in statistical literature by numerous researchers to deal with dropouts or unintentional random removals in life-testing experiments. All of them considered failure time and censoring time to be independent. But there are several situations in which one observes that as the failure time of an item increases, the censoring time decreases. In medical studies or especially in clinical trials, the occurrence of dropouts or unintentional removals is frequently observed in such a way that as the treatment (failure) time increases, the dropout (censoring) time decreases. No work has yet been found that deals with such correlated failure and censoring times. Therefore, in this article, we assume that the failure time is negatively correlated with censoring time, and they follow Gumbel’s type-I bivariate exponential distribution. We compute the maximum likelihood estimates of the model parameters. Using the Monte Carlo Markov chain methods, the Bayesian estimators of the parameters are calculated. The expected experimental time is also evaluated. Finally, for illustrative purposes, a numerical study and a real data set analysis are given.

Suggested Citation

  • Hare Krishna & Rajni Goel, 2024. "Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution," Annals of Data Science, Springer, vol. 11(4), pages 1185-1207, August.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:4:d:10.1007_s40745-023-00463-7
    DOI: 10.1007/s40745-023-00463-7
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    References listed on IDEAS

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    1. Kapil Kumar, 2018. "Classical and Bayesian estimation in log-logistic distribution under random censoring," 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(2), pages 440-451, April.
    2. Muhammad Danish & Muhammad Aslam, 2013. "Bayesian estimation for randomly censored generalized exponential distribution under asymmetric loss functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 1106-1119.
    3. M. E. Ghitany & S. Al-Awadhi, 2002. "Maximum likelihood estimation of Burr XII distribution parameters under random censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 955-965.
    4. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
    5. Kapil Kumar & Indrajeet Kumar, 2019. "Estimation in Inverse Weibull Distribution Based on Randomly Censored Data," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 47-74.
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