Classical and Bayesian estimation of the reliability function for the inverse Lindley distribution based on lower record statistics
نویسندگان
1 Department of Mathematics and Statistics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 Department of Mathematics and Statistics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
3 Department of Statistics, University of Mazandaran, Babolsar, Iran
doi
10.22034/jsmta.2024.21608.1141چکیده
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.
