Classical and Bayesian estimation of the reliability function for the inverse Lindley distribution based on lower record statistics

Document Type : Original Scientific Paper

Authors

1 Department of Mathematics and Statistics‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran

2 Department of Statistics‎, ‎University of Mazandaran‎, ‎Babolsar‎, ‎Iran

Abstract

The reliability function‎, ‎or the survival function at a specified time t‎, ‎denotes the proportion of products that remain operational beyond time t and continue to function‎. ‎This interpretation underscores the pivotal role of the survival function and its estimation in understanding lifetime phenomena‎. ‎This paper explores the estimation of the survival function for the inverse Lindley distribution based on lower records‎. ‎The estimation techniques encompass maximum likelihood and bootstrap methods‎. ‎Furthermore‎, ‎Bayesian approaches employing Metropolis-Hastings and importance sampling algorithms are employed‎. ‎In addition to deriving approximate confidence intervals using the delta method and percentile bootstrap intervals for the survival function‎, ‎Chen and Shao's shortest width credible intervals are also determined‎. ‎A comprehensive simulation study is presented to assess the effectiveness of both point and interval estimators‎. Finally‎, ‎an application of the results is given to a real data set.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 4, Issue 2
July 2023
Pages 183-198

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History

  • Receive Date: 10 May 2024
  • Revise Date: 08 August 2024
  • Accept Date: 20 August 2024

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