Reliability analysis of the Lindley distribution via unified hybrid censoring with applications in medical survival and biological lifetime data

Said G. Nassr; T. S. Taher; Tmader Alballa; Neema M. Elharoun; Said G. Nassr; T. S. Taher; Tmader Alballa; Neema M. Elharoun

doi:10.3934/math.2025670

AIMS Mathematics

2025, Volume 10, Issue 6: 14943-14974. doi: 10.3934/math.2025670

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Reliability analysis of the Lindley distribution via unified hybrid censoring with applications in medical survival and biological lifetime data

1.
Department of Statistics and Insurance, Faculty of Commerce, Arish University, Al-Arish 45511, Egypt
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 21 April 2025 Revised: 03 June 2025 Accepted: 18 June 2025 Published: 30 June 2025
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

Unified hybrid censored sampling results from the need to effectively evaluate survival data impacted by different censoring techniques, enabling researchers to use partial information and lower bias in parameter estimates. This study employs unified hybrid censored samples to examine the maximum likelihood and Bayesian estimation methods for unknown parameters of the Lindley distribution, encompassing the reliability function, hazard rate function, cumulative hazard function, and mean residual life. Initially, we estimate the model parameters via the maximum likelihood method. We also examine bootstrapped confidence intervals and asymptotic confidence intervals for unknown parameters of the Lindley distribution. We also derive the confidence interval for the mean residual life, the hazard rate function, the cumulative hazard function, and the reliability function. Moreover, using flexible gamma priors for parameters combined with a non-informative prior yields Bayes estimators based on the principles of squared error, linear exponential, and general entropy loss functions. Consequently, we identify the corresponding highest posterior density credible intervals for unknown parameters, the reliability function, the hazard rate function, the cumulative hazard function, and the mean residual lifetime. Using numerous criteria, Monte Carlo simulations help evaluate the accuracy of the given estimations. We also assess sampling techniques across different rival censoring systems, including bootstrap and censored samples. Ultimately, we investigated a medical data set to show the useful value of the suggested approaches. The numerical results confirm the efficiency of our proposed approaches.
- Lindley distribution,
- unified hybrid censored sampling,
- Bayesian estimation,
- maximum likelihood estimation,
- Monte Carlo simulation,
- Bootstrapping sample
Citation: Said G. Nassr, T. S. Taher, Tmader Alballa, Neema M. Elharoun. Reliability analysis of the Lindley distribution via unified hybrid censoring with applications in medical survival and biological lifetime data[J]. AIMS Mathematics, 2025, 10(6): 14943-14974. doi: 10.3934/math.2025670

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Abstract

Unified hybrid censored sampling results from the need to effectively evaluate survival data impacted by different censoring techniques, enabling researchers to use partial information and lower bias in parameter estimates. This study employs unified hybrid censored samples to examine the maximum likelihood and Bayesian estimation methods for unknown parameters of the Lindley distribution, encompassing the reliability function, hazard rate function, cumulative hazard function, and mean residual life. Initially, we estimate the model parameters via the maximum likelihood method. We also examine bootstrapped confidence intervals and asymptotic confidence intervals for unknown parameters of the Lindley distribution. We also derive the confidence interval for the mean residual life, the hazard rate function, the cumulative hazard function, and the reliability function. Moreover, using flexible gamma priors for parameters combined with a non-informative prior yields Bayes estimators based on the principles of squared error, linear exponential, and general entropy loss functions. Consequently, we identify the corresponding highest posterior density credible intervals for unknown parameters, the reliability function, the hazard rate function, the cumulative hazard function, and the mean residual lifetime. Using numerous criteria, Monte Carlo simulations help evaluate the accuracy of the given estimations. We also assess sampling techniques across different rival censoring systems, including bootstrap and censored samples. Ultimately, we investigated a medical data set to show the useful value of the suggested approaches. The numerical results confirm the efficiency of our proposed approaches.

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